Least Common Multiple of 457 and 460

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 457 and 460 the smallest integer that is 210220 that is divisible by both numbers.

Least Common Multiple (LCM) of 457 and 460 is 210220.

LCM(457,460) = 210220

LCM of 457 and 460

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

LCM of:
and

Least Common Multiple of 457 and 460

LCM of 457 and 460 is 210220

Least common multiple can be found by multiplying the highest exponent prime factors of 457 and 460. First we will calculate the prime factors of 457 and 460.

Prime Factorization of 457


457 457
1

Prime factors of 457 are 457. Prime factorization of 457 in exponential form is:

457 = 4571

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

Now multiplying the highest exponent prime factors to calculate the LCM of 457 and 460.

LCM(457,460) = 22×51×231×4571
LCM(457,460) = 210220

Factors of 457

List of positive integer factors of 457 that divides 457 without a remainder.

1, 457

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

Least Common Multiple of 457 and 460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 457 and 460, than apply into the LCM equation.

GCF(457,460) = 1
LCM(457,460) = ( 457 × 460) / 1
LCM(457,460) = 210220 / 1
LCM(457,460) = 210220

Properties of LCM 457 and 460

(i) The LCM of 460 and 457 is associative

LCM of 457 and 460 = LCM of 460 and 457

Related Least Common Multiples of 457

Related Least Common Multiples of 460

Frequently Asked Questions on LCM of 457 and 460

1. What is the LCM of 457 and 460?

Answer: LCM of 457 and 460 is 210220.

2. What are the Factors of 457?

Answer: Factors of 457 are 1, 457. There are 2 integers that are factors of 457. The greatest factor of 457 is 457.

3. 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.

4. How to Find the LCM of 457 and 460?

Answer:

Least Common Multiple of 457 and 460 = 210220

Step 1: Find the prime factorization of 457

457 = 457

Step 2: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

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

LCM = 210220 = 2 x 2 x 5 x 23 x 457

Step 4: Therefore, the least common multiple of 457 and 460 is 210220.