Least Common Multiple of 460 and 462

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 462 the smallest integer that is 106260 that is divisible by both numbers.

Least Common Multiple (LCM) of 460 and 462 is 106260.

LCM(460,462) = 106260

LCM of 460 and 462

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

LCM of:
and

Least Common Multiple of 460 and 462

LCM of 460 and 462 is 106260

Least common multiple can be found by multiplying the highest exponent prime factors of 460 and 462. First we will calculate the prime factors of 460 and 462.

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 462


2 462
3 231
7 77
11 11
1

Prime factors of 462 are 2, 3, 7,11. Prime factorization of 462 in exponential form is:

462 = 21×31×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 460 and 462.

LCM(460,462) = 22×31×51×71×111×231
LCM(460,462) = 106260

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 462

List of positive integer factors of 462 that divides 462 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462

Least Common Multiple of 460 and 462 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 462, than apply into the LCM equation.

GCF(460,462) = 2
LCM(460,462) = ( 460 × 462) / 2
LCM(460,462) = 212520 / 2
LCM(460,462) = 106260

Properties of LCM 460 and 462

(i) The LCM of 462 and 460 is associative

LCM of 460 and 462 = LCM of 462 and 460

Related Least Common Multiples of 460

Related Least Common Multiples of 462

Frequently Asked Questions on LCM of 460 and 462

1. What is the LCM of 460 and 462?

Answer: LCM of 460 and 462 is 106260.

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 462?

Answer: Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462. There are 16 integers that are factors of 462. The greatest factor of 462 is 462.

4. How to Find the LCM of 460 and 462?

Answer:

Least Common Multiple of 460 and 462 = 106260

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 462

462 = 2 x 3 x 7 x 11

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

LCM = 106260 = 2 x 2 x 3 x 5 x 7 x 11 x 23

Step 4: Therefore, the least common multiple of 460 and 462 is 106260.