# What is the LCM of 4, 9, and 10?

LCM of 4, 9, and 10 is the smallest number which divides three of them exactly without leaving a remainder.

## Answer: LCM of 4, 9, and 10 is 180

For 4, 9, and 10, the smallest number that is perfectly divisible by all of them is their LCM.

## Explanation:

Let us see how to calculate it below:

Least Common Multiple of 4, 9, and 10 is the smallest number that will completely divide them.

### LCM of 4, 9, and 10 using Common Division Method

In this method, we divide 4, 9 and 10 concurrently with prime numbers until we don't have a prime number to divide them further. Product of the prime numbers used in dividing 4,9 and 10 is their LCM

### LCM of 4, 9, and 10 by using Prime factorization:

In this method, we write all the given numbers as the product of its prime factors and then multiply the common and uncommon factors to get the LCM.

Prime factorization of 4=2×2= 2^{2}

Prime factorization of 9=3×3= 3^{2}, and

Prime factorization of 10 =5×2

The prime factors 2 and 3 occur twice and prime factor 5 occur once in the prime factorization.

So, the product of all these prime factors is the LCM of 4, 9, and 10, which is 2^{2 }×3^{2 }×5 = 180.