Least Common Multiple of 456 and 460

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 456 and 460 the smallest integer that is 52440 that is divisible by both numbers.

Least Common Multiple (LCM) of 456 and 460 is 52440.

LCM(456,460) = 52440

LCM of 456 and 460

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 456 and 460

LCM of 456 and 460 is 52440

Least common multiple can be found by multiplying the highest exponent prime factors of 456 and 460. First we will calculate the prime factors of 456 and 460.

Prime Factorization of 456


2 456
2 228
2 114
3 57
19 19
1

Prime factors of 456 are 2, 3,19. Prime factorization of 456 in exponential form is:

456 = 23×31×191

Prime Factorization of 460


2 460
2 230
5 115
23 23
1

Prime factors of 460 are 2, 5,23. Prime factorization of 460 in exponential form is:

460 = 22×51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 456 and 460.

LCM(456,460) = 23×31×51×191×231
LCM(456,460) = 52440

Factors of 456

List of positive integer factors of 456 that divides 456 without a remainder.

1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456

Factors of 460

List of positive integer factors of 460 that divides 460 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460

Least Common Multiple of 456 and 460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 456 and 460, than apply into the LCM equation.

GCF(456,460) = 4
LCM(456,460) = ( 456 × 460) / 4
LCM(456,460) = 209760 / 4
LCM(456,460) = 52440

Properties of LCM 456 and 460

(i) The LCM of 460 and 456 is associative

LCM of 456 and 460 = LCM of 460 and 456

Related Least Common Multiples of 456

Related Least Common Multiples of 460

Frequently Asked Questions on LCM of 456 and 460

1. What is the LCM of 456 and 460?

Answer: LCM of 456 and 460 is 52440.

2. What are the Factors of 456?

Answer: Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. There are 16 integers that are factors of 456. The greatest factor of 456 is 456.

3. What are the Factors of 460?

Answer: Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460. There are 12 integers that are factors of 460. The greatest factor of 460 is 460.

4. How to Find the LCM of 456 and 460?

Answer:

Least Common Multiple of 456 and 460 = 52440

Step 1: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

Step 2: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 52440 = 2 x 2 x 2 x 3 x 5 x 19 x 23

Step 4: Therefore, the least common multiple of 456 and 460 is 52440.