LCM of 3 and 15 is the smallest number among all common multiples of 3 and 15. The first few multiples of 3 and 15 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (15, 30, 45, 60, 75, 90, 105, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 15 - by listing multiples, by division method, and by prime factorization.

You are watching: Common multiples of 3 and 15

 1 LCM of 3 and 15 2 List of Methods 3 Solved Examples 4 FAQs

Answer: LCM of 3 and 15 is 15. Explanation:

The LCM of two non-zero integers, x(3) and y(15), is the smallest positive integer m(15) that is divisible by both x(3) and y(15) without any remainder.

The methods to find the LCM of 3 and 15 are explained below.

By Division MethodBy Listing MultiplesBy Prime Factorization Method

### LCM of 3 and 15 by Division Method To calculate the LCM of 3 and 15 by the division method, we will divide the numbers(3, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 15.

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

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

### LCM of 3 and 15 by Listing Multiples To calculate the LCM of 3 and 15 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 15 (15, 30, 45, 60, 75, 90, 105, . . . . )Step 2: The common multiples from the multiples of 3 and 15 are 15, 30, . . .Step 3: The smallest common multiple of 3 and 15 is 15.

∴ The least common multiple of 3 and 15 = 15.

See more: What Is The Graph Of 3X + 5Y = –15? What Is The Graph Of 3X + 5Y =

### LCM of 3 and 15 by Prime Factorization

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