Least Common Multiple of 460 and 464

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 464 the smallest integer that is 53360 that is divisible by both numbers.

Least Common Multiple (LCM) of 460 and 464 is 53360.

LCM(460,464) = 53360

LCM of 460 and 464

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

LCM of:
and

Least Common Multiple of 460 and 464

LCM of 460 and 464 is 53360

Least common multiple can be found by multiplying the highest exponent prime factors of 460 and 464. First we will calculate the prime factors of 460 and 464.

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 464


2 464
2 232
2 116
2 58
29 29
1

Prime factors of 464 are 2,29. Prime factorization of 464 in exponential form is:

464 = 24×291

Now multiplying the highest exponent prime factors to calculate the LCM of 460 and 464.

LCM(460,464) = 24×51×231×291
LCM(460,464) = 53360

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 464

List of positive integer factors of 464 that divides 464 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 232, 464

Least Common Multiple of 460 and 464 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 464, than apply into the LCM equation.

GCF(460,464) = 4
LCM(460,464) = ( 460 × 464) / 4
LCM(460,464) = 213440 / 4
LCM(460,464) = 53360

Properties of LCM 460 and 464

(i) The LCM of 464 and 460 is associative

LCM of 460 and 464 = LCM of 464 and 460

Related Least Common Multiples of 460

Related Least Common Multiples of 464

Frequently Asked Questions on LCM of 460 and 464

1. What is the LCM of 460 and 464?

Answer: LCM of 460 and 464 is 53360.

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 464?

Answer: Factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464. There are 10 integers that are factors of 464. The greatest factor of 464 is 464.

4. How to Find the LCM of 460 and 464?

Answer:

Least Common Multiple of 460 and 464 = 53360

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 464

464 = 2 x 2 x 2 x 2 x 29

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

LCM = 53360 = 2 x 2 x 2 x 2 x 5 x 23 x 29

Step 4: Therefore, the least common multiple of 460 and 464 is 53360.