Here are the step-by-step calculations to find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) for each pair of numbers.
1. Pair: 60, 66
*
GCF:
* Factors of 60: 1, 2, 3, 4, 5,
6, 10, 12, 15, 20, 30, 60
* Factors of 66: 1, 2, 3,
6, 11, 22, 33, 66
* The largest number in both lists is
6.
*
LCM:
* Multiples of 60: 60, 120, 180, 240, 300,
330, 390...
* Multiples of 66: 66, 132, 198, 264,
330, 396...
* The first number they share is
330.
2. Pair: 44, 14
*
GCF:
* Factors of 44: 1,
2, 4, 11, 22, 44
* Factors of 14: 1,
2, 7, 14
* The largest common factor is
2.
*
LCM:
* Multiples of 44: 44, 88, 132, 176, 220, 264,
308...
* Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294,
308...
* The first match is
308.
3. Pair: 7, 56
*
GCF:
* Since 7 goes into 56 evenly ($7 \times 8 = 56$), the greatest common factor is the smaller number,
7.
*
LCM:
* Since 56 is a multiple of 7, the least common multiple is the larger number,
56.
4. Pair: 20, 22
*
GCF:
* Factors of 20: 1,
2, 4, 5, 10, 20
* Factors of 22: 1,
2, 11, 22
* The largest common factor is
2.
*
LCM:
* Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220...
* Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198,
220...
* The first match is
220.
5. Pair: 13, 31
*
GCF:
* Both 13 and 31 are prime numbers (they can only be divided by 1 and themselves). They share no factors other than 1.
* GCF is
1.
*
LCM:
* Because they are prime numbers, you just multiply them together: $13 \times 31$.
* $13 \times 31 =$
403.
6. Pair: 8, 42
*
GCF:
* Factors of 8: 1,
2, 4, 8
* Factors of 42: 1,
2, 3, 6, 7, 14, 21, 42
* The largest common factor is
2.
*
LCM:
* Multiples of 42: 42, 84, 126, 168...
* Check if 168 is divisible by 8: $168 \div 8 = 21$. Yes.
* LCM is
168.
7. Pair: 16, 60
*
GCF:
* Factors of 16: 1, 2,
4, 8, 16
* Factors of 60: 1, 2, 3,
4, 5, 6, 10, 12, 15, 20, 30, 60
* The largest common factor is
4.
*
LCM:
* Multiples of 60: 60, 120, 180, 240...
* Check if 240 is divisible by 16: $240 \div 16 = 15$. Yes.
* LCM is
240.
Final Answer:
1. GCF: 6, LCM: 330
2. GCF: 2, LCM: 308
3. GCF: 7, LCM: 56
4. GCF: 2, LCM: 220
5. GCF: 1, LCM: 403
6. GCF: 2, LCM: 168
7. GCF: 4, LCM: 240
Parent Tip: Review the logic above to help your child master the concept of gcd lcm worksheets.
