Worksheet for practicing finding the greatest common factor and least common multiple of number pairs.
Educational worksheet: Least Common Multiple and Greatest Common Factor Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Least Common Multiple and Greatest Common Factor Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Least Common Multiple and Greatest Common Factor Worksheets
Here are the step-by-step solutions for each problem on the worksheet. I have used the "cake method" (also known as the ladder method) to find the Greatest Common Factor (GCF) and Least Common Multiple (LCM).
1. 22 and 30
* Step 1: Both numbers are even, so divide by 2.
* $22 \div 2 = 11$
* $30 \div 2 = 15$
* Step 2: Look at 11 and 15. They share no common factors other than 1, so we stop.
* GCF: Multiply the numbers on the outside left: 2.
* LCM: Multiply the outside left number and the bottom numbers: $2 \times 11 \times 15 = 2 \times 165 =$ 330.
2. 12 and 66
* Step 1: Both are even, divide by 2.
* $12 \div 2 = 6$
* $66 \div 2 = 33$
* Step 2: Look at 6 and 33. Both are divisible by 3.
* $6 \div 3 = 2$
* $33 \div 3 = 11$
* Step 3: Look at 2 and 11. No common factors. Stop.
* GCF: Multiply the divisors on the left: $2 \times 3 =$ 6.
* LCM: Multiply everything: $2 \times 3 \times 2 \times 11 = 12 \times 11 =$ 132.
3. 36 and 40
* Step 1: Both are even, divide by 2.
* $36 \div 2 = 18$
* $40 \div 2 = 20$
* Step 2: 18 and 20 are still even, divide by 2 again.
* $18 \div 2 = 9$
* $20 \div 2 = 10$
* Step 3: 9 and 10 share no common factors. Stop.
* GCF: Multiply the left side: $2 \times 2 =$ 4.
* LCM: Multiply all around: $2 \times 2 \times 9 \times 10 = 4 \times 90 =$ 360.
4. 20 and 50
* Step 1: Both end in 0, so divide by 10 (or do 2 then 5). Let's do 10.
* $20 \div 10 = 2$
* $50 \div 10 = 5$
* Step 2: 2 and 5 have no common factors. Stop.
* GCF: The divisor on the left is 10.
* LCM: $10 \times 2 \times 5 = 10 \times 10 =$ 100.
5. 15 and 45
* Step 1: Both are divisible by 5.
* $15 \div 5 = 3$
* $45 \div 5 = 9$
* Step 2: 3 and 9 are both divisible by 3.
* $3 \div 3 = 1$
* $9 \div 3 = 3$
* Step 3: 1 and 3 have no common factors. Stop.
* GCF: Multiply the left side: $5 \times 3 =$ 15.
* LCM: Multiply all around: $5 \times 3 \times 1 \times 3 = 15 \times 3 =$ 45.
6. 32 and 50
* Step 1: Both are even, divide by 2.
* $32 \div 2 = 16$
* $50 \div 2 = 25$
* Step 2: 16 and 25 share no common factors ($16=2^4$, $25=5^2$). Stop.
* GCF: The divisor on the left is 2.
* LCM: $2 \times 16 \times 25$. Since $2 \times 25 = 50$, then $50 \times 16 =$ 800.
7. 28 and 42
* Step 1: Both are even, divide by 2.
* $28 \div 2 = 14$
* $42 \div 2 = 21$
* Step 2: 14 and 21 are both divisible by 7.
* $14 \div 7 = 2$
* $21 \div 7 = 3$
* Step 3: 2 and 3 have no common factors. Stop.
* GCF: Multiply the left side: $2 \times 7 =$ 14.
* LCM: Multiply all around: $2 \times 7 \times 2 \times 3 = 14 \times 6 =$ 84.
8. 75 and 200
* Step 1: Both end in 0 or 5, so divide by 25 (or do 5 twice). Let's use 25.
* $75 \div 25 = 3$
* $200 \div 25 = 8$
* Step 2: 3 and 8 have no common factors. Stop.
* GCF: The divisor on the left is 25.
* LCM: $25 \times 3 \times 8$. Since $25 \times 8 = 200$, then $200 \times 3 =$ 600.
Final Answer:
1. GCF: 2, LCM: 330
2. GCF: 6, LCM: 132
3. GCF: 4, LCM: 360
4. GCF: 10, LCM: 100
5. GCF: 15, LCM: 45
6. GCF: 2, LCM: 800
7. GCF: 14, LCM: 84
8. GCF: 25, LCM: 600
1. 22 and 30
* Step 1: Both numbers are even, so divide by 2.
* $22 \div 2 = 11$
* $30 \div 2 = 15$
* Step 2: Look at 11 and 15. They share no common factors other than 1, so we stop.
* GCF: Multiply the numbers on the outside left: 2.
* LCM: Multiply the outside left number and the bottom numbers: $2 \times 11 \times 15 = 2 \times 165 =$ 330.
2. 12 and 66
* Step 1: Both are even, divide by 2.
* $12 \div 2 = 6$
* $66 \div 2 = 33$
* Step 2: Look at 6 and 33. Both are divisible by 3.
* $6 \div 3 = 2$
* $33 \div 3 = 11$
* Step 3: Look at 2 and 11. No common factors. Stop.
* GCF: Multiply the divisors on the left: $2 \times 3 =$ 6.
* LCM: Multiply everything: $2 \times 3 \times 2 \times 11 = 12 \times 11 =$ 132.
3. 36 and 40
* Step 1: Both are even, divide by 2.
* $36 \div 2 = 18$
* $40 \div 2 = 20$
* Step 2: 18 and 20 are still even, divide by 2 again.
* $18 \div 2 = 9$
* $20 \div 2 = 10$
* Step 3: 9 and 10 share no common factors. Stop.
* GCF: Multiply the left side: $2 \times 2 =$ 4.
* LCM: Multiply all around: $2 \times 2 \times 9 \times 10 = 4 \times 90 =$ 360.
4. 20 and 50
* Step 1: Both end in 0, so divide by 10 (or do 2 then 5). Let's do 10.
* $20 \div 10 = 2$
* $50 \div 10 = 5$
* Step 2: 2 and 5 have no common factors. Stop.
* GCF: The divisor on the left is 10.
* LCM: $10 \times 2 \times 5 = 10 \times 10 =$ 100.
5. 15 and 45
* Step 1: Both are divisible by 5.
* $15 \div 5 = 3$
* $45 \div 5 = 9$
* Step 2: 3 and 9 are both divisible by 3.
* $3 \div 3 = 1$
* $9 \div 3 = 3$
* Step 3: 1 and 3 have no common factors. Stop.
* GCF: Multiply the left side: $5 \times 3 =$ 15.
* LCM: Multiply all around: $5 \times 3 \times 1 \times 3 = 15 \times 3 =$ 45.
6. 32 and 50
* Step 1: Both are even, divide by 2.
* $32 \div 2 = 16$
* $50 \div 2 = 25$
* Step 2: 16 and 25 share no common factors ($16=2^4$, $25=5^2$). Stop.
* GCF: The divisor on the left is 2.
* LCM: $2 \times 16 \times 25$. Since $2 \times 25 = 50$, then $50 \times 16 =$ 800.
7. 28 and 42
* Step 1: Both are even, divide by 2.
* $28 \div 2 = 14$
* $42 \div 2 = 21$
* Step 2: 14 and 21 are both divisible by 7.
* $14 \div 7 = 2$
* $21 \div 7 = 3$
* Step 3: 2 and 3 have no common factors. Stop.
* GCF: Multiply the left side: $2 \times 7 =$ 14.
* LCM: Multiply all around: $2 \times 7 \times 2 \times 3 = 14 \times 6 =$ 84.
8. 75 and 200
* Step 1: Both end in 0 or 5, so divide by 25 (or do 5 twice). Let's use 25.
* $75 \div 25 = 3$
* $200 \div 25 = 8$
* Step 2: 3 and 8 have no common factors. Stop.
* GCF: The divisor on the left is 25.
* LCM: $25 \times 3 \times 8$. Since $25 \times 8 = 200$, then $200 \times 3 =$ 600.
Final Answer:
1. GCF: 2, LCM: 330
2. GCF: 6, LCM: 132
3. GCF: 4, LCM: 360
4. GCF: 10, LCM: 100
5. GCF: 15, LCM: 45
6. GCF: 2, LCM: 800
7. GCF: 14, LCM: 84
8. GCF: 25, LCM: 600
Parent Tip: Review the logic above to help your child master the concept of gcd lcm worksheets.
