To find the Least Common Multiple (LCM) for each pair, we look for the smallest number that both numbers can divide into evenly. Here is the step-by-step solution for each problem:
1.
2, 4
* Multiples of 2: 2, 4, 6...
* Multiples of 4: 4, 8...
* The smallest match is
4.
2.
20, 24
* Prime factorization of 20: $2 \times 2 \times 5$
* Prime factorization of 24: $2 \times 2 \times 2 \times 3$
* LCM needs three 2s, one 3, and one 5: $2 \times 2 \times 2 \times 3 \times 5 = 120$.
* Answer:
120
3.
30, 24
* Prime factorization of 30: $2 \times 3 \times 5$
* Prime factorization of 24: $2 \times 2 \times 2 \times 3$
* LCM needs three 2s, one 3, and one 5: $2 \times 2 \times 2 \times 3 \times 5 = 120$.
* Answer:
120
4.
30, 4
* Multiples of 30: 30, 60, 90...
* 60 is divisible by 4 ($60 \div 4 = 15$).
* Answer:
60
5.
15, 10
* Multiples of 15: 15, 30...
* 30 is divisible by 10 ($30 \div 10 = 3$).
* Answer:
30
6.
20, 3
* Since 3 is a prime number and doesn't go into 20, just multiply them.
* $20 \times 3 = 60$.
* Answer:
60
7.
12, 60
* Check if the larger number (60) is divisible by the smaller number (12).
* $12 \times 5 = 60$. It works!
* Answer:
60
8.
15, 20
* Multiples of 20: 20, 40, 60...
* 60 is divisible by 15 ($15 \times 4 = 60$).
* Answer:
60
9.
8, 15
* These numbers share no common factors other than 1. Multiply them together.
* $8 \times 15 = 120$.
* Answer:
120
10.
24, 30
* Prime factorization of 24: $2 \times 2 \times 2 \times 3$
* Prime factorization of 30: $2 \times 3 \times 5$
* LCM needs three 2s, one 3, and one 5: $2 \times 2 \times 2 \times 3 \times 5 = 120$.
* Answer:
120
Final Answer:
2, 4:
4
20, 24:
120
30, 24:
120
30, 4:
60
15, 10:
30
20, 3:
60
12, 60:
60
15, 20:
60
8, 15:
120
24, 30:
120
Parent Tip: Review the logic above to help your child master the concept of lcm worksheets.
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