GCF and LCM?

Question

I need to find a formula that will enable me to easily predict the LCM (Least common multiple) of any pair of whole numbers from the two numbers themselves and their GCF (greatest common factor).

Answer 1

The product of the LCM and the GCF of any two numbers is equal to the product of the two numbers themselves. So to find the LCM, just multiply the two numbers together and then divide their product by the GCF.

Answer 2

The least common multiple, or LCM, is another number that's useful in solving many math problems. Let's find the LCM of 30 and 45. One way to find the least common multiple of two numbers is to first list the prime factors of each number.

30 = 2 × 3 × 5
45 = 3 × 3 × 5

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

2: one occurrence
3: two occurrences
5: one occurrence
2 × 3 × 3 × 5 = 90 <— LCM

After you've calculated a least common multiple, always check to be sure your answer can be divided evenly by both numbers.

Answer 3

Theres an easy formula : lcm(x,y) = xy/gcf(x,y).