Least Common Multiple of 456 and 464

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 464 the smallest integer that is 26448 that is divisible by both numbers.

Least Common Multiple (LCM) of 456 and 464 is 26448.

LCM(456,464) = 26448

LCM of 456 and 464

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

LCM of:
and

Least Common Multiple of 456 and 464

LCM of 456 and 464 is 26448

Least common multiple can be found by multiplying the highest exponent prime factors of 456 and 464. First we will calculate the prime factors of 456 and 464.

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 464


2 464
2 232
2 116
2 58
29 29
1

Prime factors of 464 are 2,29. Prime factorization of 464 in exponential form is:

464 = 24×291

Now multiplying the highest exponent prime factors to calculate the LCM of 456 and 464.

LCM(456,464) = 24×31×191×291
LCM(456,464) = 26448

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 464

List of positive integer factors of 464 that divides 464 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 232, 464

Least Common Multiple of 456 and 464 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 464, than apply into the LCM equation.

GCF(456,464) = 8
LCM(456,464) = ( 456 × 464) / 8
LCM(456,464) = 211584 / 8
LCM(456,464) = 26448

Properties of LCM 456 and 464

(i) The LCM of 464 and 456 is associative

LCM of 456 and 464 = LCM of 464 and 456

Related Least Common Multiples of 456

Related Least Common Multiples of 464

Frequently Asked Questions on LCM of 456 and 464

1. What is the LCM of 456 and 464?

Answer: LCM of 456 and 464 is 26448.

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 464?

Answer: Factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464. There are 10 integers that are factors of 464. The greatest factor of 464 is 464.

4. How to Find the LCM of 456 and 464?

Answer:

Least Common Multiple of 456 and 464 = 26448

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 464

464 = 2 x 2 x 2 x 2 x 29

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

LCM = 26448 = 2 x 2 x 2 x 2 x 3 x 19 x 29

Step 4: Therefore, the least common multiple of 456 and 464 is 26448.