Least Common Multiple of 456 and 457

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 457 the smallest integer that is 208392 that is divisible by both numbers.

Least Common Multiple (LCM) of 456 and 457 is 208392.

LCM(456,457) = 208392

LCM of 456 and 457

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

LCM of:
and

Least Common Multiple of 456 and 457

LCM of 456 and 457 is 208392

Least common multiple can be found by multiplying the highest exponent prime factors of 456 and 457. First we will calculate the prime factors of 456 and 457.

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 457


457 457
1

Prime factors of 457 are 457. Prime factorization of 457 in exponential form is:

457 = 4571

Now multiplying the highest exponent prime factors to calculate the LCM of 456 and 457.

LCM(456,457) = 23×31×191×4571
LCM(456,457) = 208392

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 457

List of positive integer factors of 457 that divides 457 without a remainder.

1, 457

Least Common Multiple of 456 and 457 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 457, than apply into the LCM equation.

GCF(456,457) = 1
LCM(456,457) = ( 456 × 457) / 1
LCM(456,457) = 208392 / 1
LCM(456,457) = 208392

Properties of LCM 456 and 457

(i) The LCM of 457 and 456 is associative

LCM of 456 and 457 = LCM of 457 and 456

Related Least Common Multiples of 456

Related Least Common Multiples of 457

Frequently Asked Questions on LCM of 456 and 457

1. What is the LCM of 456 and 457?

Answer: LCM of 456 and 457 is 208392.

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 457?

Answer: Factors of 457 are 1, 457. There are 2 integers that are factors of 457. The greatest factor of 457 is 457.

4. How to Find the LCM of 456 and 457?

Answer:

Least Common Multiple of 456 and 457 = 208392

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 457

457 = 457

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

LCM = 208392 = 2 x 2 x 2 x 3 x 19 x 457

Step 4: Therefore, the least common multiple of 456 and 457 is 208392.