What is the lowest common multiple of 10 and 12?
There are two strategies I like to use for finding the Least Common Multiple.
1. Lists of multiples. Make a list of the multiples of each number. Find the smallest number that is in common on both lists.
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, .. 12: 12,24,36,48,60,
I can stop now. 60 is in common on both lists, so the LCM of 10 and 12 is 60.
2. Prime factorization. Write each number in prime factored form. Then select all the primes that were used in either number and select the largest exponent used on any prime number from either prime factorization.
10 = 2 x 5
12 = 2² x 3
All primes used in either number: 2, 3, 5.
Largest exponent in each case: for 2 it is ², for 3 and 5 it is an unwritten ˡ.
2² x 3 ˡ x 5 ˡ = 60. So the LCM of 10 and 12 is 60.
There are two strategies I like to use for finding the Least Common Multiple.
1. Lists of multiples. Make a list of the multiples of each number. Find the smallest number that is in common on both lists.
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, .. 12: 12,24,36,48,60,
I can stop now. 60 is in common on both lists, so the LCM of 10 and 12 is 60.
2. Prime factorization. Write each number in prime factored form. Then select all the primes that were used in either number and select the largest exponent used on any prime number from either prime factorization.
10 = 2 x 5
12 = 2² x 3
All primes used in either number: 2, 3, 5.
Largest exponent in each case: for 2 it is ², for 3 and 5 it is an unwritten ˡ.
2² x 3 ˡ x 5 ˡ = 60. So the LCM of 10 and 12 is 60.