Least Common Multiple of 460 and 468

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 460 and 468 the smallest integer that is 53820 that is divisible by both numbers.

Least Common Multiple (LCM) of 460 and 468 is 53820.

LCM(460,468) = 53820

LCM of 460 and 468

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

LCM of:
and

Least Common Multiple of 460 and 468

LCM of 460 and 468 is 53820

Least common multiple can be found by multiplying the highest exponent prime factors of 460 and 468. First we will calculate the prime factors of 460 and 468.

Prime Factorization of 460


2 460
2 230
5 115
23 23
1

Prime factors of 460 are 2, 5,23. Prime factorization of 460 in exponential form is:

460 = 22×51×231

Prime Factorization of 468


2 468
2 234
3 117
3 39
13 13
1

Prime factors of 468 are 2, 3,13. Prime factorization of 468 in exponential form is:

468 = 22×32×131

Now multiplying the highest exponent prime factors to calculate the LCM of 460 and 468.

LCM(460,468) = 22×32×51×131×231
LCM(460,468) = 53820

Factors of 460

List of positive integer factors of 460 that divides 460 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460

Factors of 468

List of positive integer factors of 468 that divides 468 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468

Least Common Multiple of 460 and 468 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 460 and 468, than apply into the LCM equation.

GCF(460,468) = 4
LCM(460,468) = ( 460 × 468) / 4
LCM(460,468) = 215280 / 4
LCM(460,468) = 53820

Properties of LCM 460 and 468

(i) The LCM of 468 and 460 is associative

LCM of 460 and 468 = LCM of 468 and 460

Related Least Common Multiples of 460

Related Least Common Multiples of 468

Frequently Asked Questions on LCM of 460 and 468

1. What is the LCM of 460 and 468?

Answer: LCM of 460 and 468 is 53820.

2. What are the Factors of 460?

Answer: Factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460. There are 12 integers that are factors of 460. The greatest factor of 460 is 460.

3. What are the Factors of 468?

Answer: Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468. There are 18 integers that are factors of 468. The greatest factor of 468 is 468.

4. How to Find the LCM of 460 and 468?

Answer:

Least Common Multiple of 460 and 468 = 53820

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 468

468 = 2 x 2 x 3 x 3 x 13

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

LCM = 53820 = 2 x 2 x 3 x 3 x 5 x 13 x 23

Step 4: Therefore, the least common multiple of 460 and 468 is 53820.