Least Common Multiple of 450 and 458

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 458 the smallest integer that is 103050 that is divisible by both numbers.

Least Common Multiple (LCM) of 450 and 458 is 103050.

LCM(450,458) = 103050

LCM of 450 and 458

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

LCM of:
and

Least Common Multiple of 450 and 458

LCM of 450 and 458 is 103050

Least common multiple can be found by multiplying the highest exponent prime factors of 450 and 458. First we will calculate the prime factors of 450 and 458.

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 458


2 458
229 229
1

Prime factors of 458 are 2,229. Prime factorization of 458 in exponential form is:

458 = 21×2291

Now multiplying the highest exponent prime factors to calculate the LCM of 450 and 458.

LCM(450,458) = 21×32×52×2291
LCM(450,458) = 103050

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 458

List of positive integer factors of 458 that divides 458 without a remainder.

1, 2, 229, 458

Least Common Multiple of 450 and 458 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 458, than apply into the LCM equation.

GCF(450,458) = 2
LCM(450,458) = ( 450 × 458) / 2
LCM(450,458) = 206100 / 2
LCM(450,458) = 103050

Properties of LCM 450 and 458

(i) The LCM of 458 and 450 is associative

LCM of 450 and 458 = LCM of 458 and 450

Related Least Common Multiples of 450

Related Least Common Multiples of 458

Frequently Asked Questions on LCM of 450 and 458

1. What is the LCM of 450 and 458?

Answer: LCM of 450 and 458 is 103050.

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 458?

Answer: Factors of 458 are 1, 2, 229, 458. There are 4 integers that are factors of 458. The greatest factor of 458 is 458.

4. How to Find the LCM of 450 and 458?

Answer:

Least Common Multiple of 450 and 458 = 103050

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 458

458 = 2 x 229

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

LCM = 103050 = 2 x 3 x 3 x 5 x 5 x 229

Step 4: Therefore, the least common multiple of 450 and 458 is 103050.