Examples
Example 1: Find the LCM of 16, 24 and 32.
Solution:
Prime factorization of 16: 16 = 2, 2, 2, 2
Prime factorization of 24: 24 = 2, 2, 2, 3
Prime factorization of 32: 32 = 2, 2, 2, 2, 2
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(16, 24, 32) = 96.
Example 2: Find the LCM of 5, 10 and 15.
Solution:
Prime factorization of 5: 5 = 5
Prime factorization of 10: 10 = 2, 5
Prime factorization of 15: 15 = 3, 5
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(5, 10, 15) = 30.
Example 3: Find the LCM of 7, 14 and 21.
Solution:
Prime factorization of 7: 7 = 7
Prime factorization of 14: 14 = 2, 7
Prime factorization of 21: 21 = 3, 7
Take the highest power of each prime factor and multiply them together to get LCM.
Therefore, LCM(7, 14, 21) = 42.
Exercise
1. LCM(12, 15, 20, 25) = 300
2. LCM(25, 30) = 150
3. LCM(28, 35, 42) = 420
4. LCM(9,12,18) = 36
5. LCM(12,18,24) = 72
6. LCM(16,32,48) = 96
7. LCM(15,25,35) = 525
8. LCM(21, 28, 35) = 420
9. LCM(8, 10, 12, 16) = 240
10. LCM(9, 12, 15, 18) = 180