Least Common Multiple of 460 and 466

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 466 the smallest integer that is 107180 that is divisible by both numbers.

Least Common Multiple (LCM) of 460 and 466 is 107180.

LCM(460,466) = 107180

LCM of 460 and 466

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

LCM of:
and

Least Common Multiple of 460 and 466

LCM of 460 and 466 is 107180

Least common multiple can be found by multiplying the highest exponent prime factors of 460 and 466. First we will calculate the prime factors of 460 and 466.

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 466


2 466
233 233
1

Prime factors of 466 are 2,233. Prime factorization of 466 in exponential form is:

466 = 21×2331

Now multiplying the highest exponent prime factors to calculate the LCM of 460 and 466.

LCM(460,466) = 22×51×231×2331
LCM(460,466) = 107180

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 466

List of positive integer factors of 466 that divides 466 without a remainder.

1, 2, 233, 466

Least Common Multiple of 460 and 466 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 466, than apply into the LCM equation.

GCF(460,466) = 2
LCM(460,466) = ( 460 × 466) / 2
LCM(460,466) = 214360 / 2
LCM(460,466) = 107180

Properties of LCM 460 and 466

(i) The LCM of 466 and 460 is associative

LCM of 460 and 466 = LCM of 466 and 460

Related Least Common Multiples of 460

Related Least Common Multiples of 466

Frequently Asked Questions on LCM of 460 and 466

1. What is the LCM of 460 and 466?

Answer: LCM of 460 and 466 is 107180.

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 466?

Answer: Factors of 466 are 1, 2, 233, 466. There are 4 integers that are factors of 466. The greatest factor of 466 is 466.

4. How to Find the LCM of 460 and 466?

Answer:

Least Common Multiple of 460 and 466 = 107180

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 466

466 = 2 x 233

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

LCM = 107180 = 2 x 2 x 5 x 23 x 233

Step 4: Therefore, the least common multiple of 460 and 466 is 107180.