Least Common Multiple of 450 and 456

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 450 and 456 the smallest integer that is 34200 that is divisible by both numbers.

Least Common Multiple (LCM) of 450 and 456 is 34200.

LCM(450,456) = 34200

LCM of 450 and 456

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

LCM of:
and

Least Common Multiple of 450 and 456

LCM of 450 and 456 is 34200

Least common multiple can be found by multiplying the highest exponent prime factors of 450 and 456. First we will calculate the prime factors of 450 and 456.

Prime Factorization of 450


2 450
3 225
3 75
5 25
5 5
1

Prime factors of 450 are 2, 3,5. Prime factorization of 450 in exponential form is:

450 = 21×32×52

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

Now multiplying the highest exponent prime factors to calculate the LCM of 450 and 456.

LCM(450,456) = 23×32×52×191
LCM(450,456) = 34200

Factors of 450

List of positive integer factors of 450 that divides 450 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450

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

Least Common Multiple of 450 and 456 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 450 and 456, than apply into the LCM equation.

GCF(450,456) = 6
LCM(450,456) = ( 450 × 456) / 6
LCM(450,456) = 205200 / 6
LCM(450,456) = 34200

Properties of LCM 450 and 456

(i) The LCM of 456 and 450 is associative

LCM of 450 and 456 = LCM of 456 and 450

Related Least Common Multiples of 450

Related Least Common Multiples of 456

Frequently Asked Questions on LCM of 450 and 456

1. What is the LCM of 450 and 456?

Answer: LCM of 450 and 456 is 34200.

2. What are the Factors of 450?

Answer: Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450. There are 18 integers that are factors of 450. The greatest factor of 450 is 450.

3. 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.

4. How to Find the LCM of 450 and 456?

Answer:

Least Common Multiple of 450 and 456 = 34200

Step 1: Find the prime factorization of 450

450 = 2 x 3 x 3 x 5 x 5

Step 2: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

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

LCM = 34200 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 19

Step 4: Therefore, the least common multiple of 450 and 456 is 34200.