Least Common Multiple of 3 and 6

In mathematics, the least common multiple of two rational numbers a and b is the smallest positive rational number that is an integer multiple of both a and b. Since it is a multiple, it can be divided by a and b without a remainder. If either a or b is 0, so that there is no such positive integer, then LCM(a, b) is defined to be zero. (Source: From Wikipedia).

Least common multiple of two numbers can be found by their multiples. Here we are going to learn how to find the least common multiple of two or more numbers.

Least common multiple of 3 and 6

The least common multiple of 3 and 6 can be found by finding the multiples 3 and 6.

The list of multiples of 3 and 6 are given below

The multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60.

The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

Here 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 are the common factors, among those 6 is the lowest common number.

So, 6 is the lowest common multiple of 3 and 6.

Example problems for least common multiple

Example 1

Find the least common multiple of 3 and 16

Solution

The least common multiple of 3 and 16 can be found by finding the multiples 3 and 16.

The list of multiples of 3 and 16 are given below

The multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60.

The multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160.

Here 48 is the lowest common number. So, 48 is the lowest common multiple of 3 and 16.

Example 2

Find the least common multiple of 13 and 6

Solution

The least common multiple of 13 and 6 can be found by finding the multiples 13 and 6.

The list of multiples of 13 and 6 are given below

The multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143.

The multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 72, 78, 84.

Here 78 is the lowest common number. So, 78 is the lowest common multiple of 13 and 6.

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Example 3

Find the least common multiple of 13 and 16

Solution

The least common multiple of 13 and 16 can be found by finding the multiples 13 and 16.

The list of multiples of 13 and 16 are given below

The multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208.

The multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208.

Here 208 is the lowest common number. So, 208 is the lowest common multiple of 13 and 16.