Least Common Multiple of 456 and 462

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 462 the smallest integer that is 35112 that is divisible by both numbers.

Least Common Multiple (LCM) of 456 and 462 is 35112.

LCM(456,462) = 35112

LCM of 456 and 462

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

LCM of:
and

Least Common Multiple of 456 and 462

LCM of 456 and 462 is 35112

Least common multiple can be found by multiplying the highest exponent prime factors of 456 and 462. First we will calculate the prime factors of 456 and 462.

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 462


2 462
3 231
7 77
11 11
1

Prime factors of 462 are 2, 3, 7,11. Prime factorization of 462 in exponential form is:

462 = 21×31×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 456 and 462.

LCM(456,462) = 23×31×71×111×191
LCM(456,462) = 35112

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 462

List of positive integer factors of 462 that divides 462 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462

Least Common Multiple of 456 and 462 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 462, than apply into the LCM equation.

GCF(456,462) = 6
LCM(456,462) = ( 456 × 462) / 6
LCM(456,462) = 210672 / 6
LCM(456,462) = 35112

Properties of LCM 456 and 462

(i) The LCM of 462 and 456 is associative

LCM of 456 and 462 = LCM of 462 and 456

Related Least Common Multiples of 456

Related Least Common Multiples of 462

Frequently Asked Questions on LCM of 456 and 462

1. What is the LCM of 456 and 462?

Answer: LCM of 456 and 462 is 35112.

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 462?

Answer: Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462. There are 16 integers that are factors of 462. The greatest factor of 462 is 462.

4. How to Find the LCM of 456 and 462?

Answer:

Least Common Multiple of 456 and 462 = 35112

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 462

462 = 2 x 3 x 7 x 11

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

LCM = 35112 = 2 x 2 x 2 x 3 x 7 x 11 x 19

Step 4: Therefore, the least common multiple of 456 and 462 is 35112.