Question:
The way I understand it is for 2,3,9 the least common multiple is 18. Am I right? If so, I guess the least common multiple for 3,4,7 is 105. Please let me know if I'm right so I can tell my daughter.

Thanks,

Kathy Heath

Hi Kathy,

You are right that the least common multiple, lcm, of 2, 3 & 9 is 18; I think you have a typo for the lcm {3,4,7} maybe you meant 3, 5 & 7? The lcm{ 3,4, 7} would be 84. lcm{3,5,7} = 105. What you do in general is look at the prime factors of the numbers you're dealing with and then form the lcm by taking the smallest power of each prime that is required. For example:

Find the lcm of 54, 150, 28. 54 = 2 * 3³; 30 = 2 * 3*5²; 28 = 2²*7. To find the lcm we need to make a number that has 2², 3³, 5² and a 7 in it , i.e. lcm{54,150,28] = 4*27*25*7 = 18900.

Hope this helps,

Denis