Least Common Multiple of 456 and 459

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 459 the smallest integer that is 69768 that is divisible by both numbers.

Least Common Multiple (LCM) of 456 and 459 is 69768.

LCM(456,459) = 69768

LCM of 456 and 459

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

LCM of:
and

Least Common Multiple of 456 and 459

LCM of 456 and 459 is 69768

Least common multiple can be found by multiplying the highest exponent prime factors of 456 and 459. First we will calculate the prime factors of 456 and 459.

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 459


3 459
3 153
3 51
17 17
1

Prime factors of 459 are 3,17. Prime factorization of 459 in exponential form is:

459 = 33×171

Now multiplying the highest exponent prime factors to calculate the LCM of 456 and 459.

LCM(456,459) = 23×33×171×191
LCM(456,459) = 69768

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 459

List of positive integer factors of 459 that divides 459 without a remainder.

1, 3, 9, 17, 27, 51, 153, 459

Least Common Multiple of 456 and 459 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 459, than apply into the LCM equation.

GCF(456,459) = 3
LCM(456,459) = ( 456 × 459) / 3
LCM(456,459) = 209304 / 3
LCM(456,459) = 69768

Properties of LCM 456 and 459

(i) The LCM of 459 and 456 is associative

LCM of 456 and 459 = LCM of 459 and 456

Related Least Common Multiples of 456

Related Least Common Multiples of 459

Frequently Asked Questions on LCM of 456 and 459

1. What is the LCM of 456 and 459?

Answer: LCM of 456 and 459 is 69768.

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 459?

Answer: Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459. There are 8 integers that are factors of 459. The greatest factor of 459 is 459.

4. How to Find the LCM of 456 and 459?

Answer:

Least Common Multiple of 456 and 459 = 69768

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 459

459 = 3 x 3 x 3 x 17

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

LCM = 69768 = 2 x 2 x 2 x 3 x 3 x 3 x 17 x 19

Step 4: Therefore, the least common multiple of 456 and 459 is 69768.