LCM of 15 and 18 is the smallest number among all common multiples of 15 and 18. The first few multiples of 15 and 18 are (15, 30, 45, 60, 75, 90, . . . ) and (18, 36, 54, 72, 90, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 18 - by division method, by prime factorization, and by listing multiples.

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1. | LCM of 15 and 18 |

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**Answer:** LCM of 15 and 18 is 90.

**Explanation: **

The LCM of two non-zero integers, x(15) and y(18), is the smallest positive integer m(90) that is divisible by both x(15) and y(18) without any remainder.

The methods to find the LCM of 15 and 18 are explained below.

By Listing MultiplesBy Prime Factorization MethodBy Division Method### LCM of 15 and 18 by Listing Multiples

To calculate the LCM of 15 and 18 by listing out the common multiples, we can follow the given below steps:

**Step 1:**List a few multiples of 15 (15, 30, 45, 60, 75, 90, . . . ) and 18 (18, 36, 54, 72, 90, . . . . )

**Step 2:**The common multiples from the multiples of 15 and 18 are 90, 180, . . .

**Step 3:**The smallest common multiple of 15 and 18 is 90.

∴ The least common multiple of 15 and 18 = 90.

### LCM of 15 and 18 by Prime Factorization

Prime factorization of 15 and 18 is (3 × 5) = 31 × 51 and (2 × 3 × 3) = 21 × 32 respectively. LCM of 15 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 32 × 51 = 90.Hence, the LCM of 15 and 18 by prime factorization is 90.

### LCM of 15 and 18 by Division Method

To calculate the LCM of 15 and 18 by the division method, we will divide the numbers(15, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 18.

**Step 3:**Continue the steps until only 1s are left in the last row.

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The LCM of 15 and 18 is the product of all prime numbers on the left, i.e. LCM(15, 18) by division method = 2 × 3 × 3 × 5 = 90.