The LCM of 10 and 12 is 60. The Least Common Multiple or Lowest Common Multiple is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 10 and 12, 60 is the first (least or smallest) number that is common in the set of multiples of 10 and 12. There are three methods to find the LCM of 10 and 12:

• Prime Factorisation Method: In this method, the numbers can be expressed as the product of prime numbers. Here, 10 and 12 can be expressed as; 10 = 2 x 5, 12 = 2 x 2 x 3. LCM (10, 12) = 2 x 2 x 3 x 5 = 60.

• Division Method: In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left. 2 10 12 2 5 6 3 5 3 5 5 1 x 1 1 Hence, LCM (10, 12) = 2 x 2 x 3 x 5 = 60.

• Listing the Multiples: By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, etc. The multiples of 12 are 12, 24, 36, 48, 60. The smallest number which is a multiple of both 10 and 12 is 60.

Therefore, the LCM of 10 and 12 is 60.