Least Common Multiple of 460 and 467

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 467 the smallest integer that is 214820 that is divisible by both numbers.

Least Common Multiple (LCM) of 460 and 467 is 214820.

LCM(460,467) = 214820

LCM of 460 and 467

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

LCM of:
and

Least Common Multiple of 460 and 467

LCM of 460 and 467 is 214820

Least common multiple can be found by multiplying the highest exponent prime factors of 460 and 467. First we will calculate the prime factors of 460 and 467.

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 467


467 467
1

Prime factors of 467 are 467. Prime factorization of 467 in exponential form is:

467 = 4671

Now multiplying the highest exponent prime factors to calculate the LCM of 460 and 467.

LCM(460,467) = 22×51×231×4671
LCM(460,467) = 214820

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 467

List of positive integer factors of 467 that divides 467 without a remainder.

1, 467

Least Common Multiple of 460 and 467 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 467, than apply into the LCM equation.

GCF(460,467) = 1
LCM(460,467) = ( 460 × 467) / 1
LCM(460,467) = 214820 / 1
LCM(460,467) = 214820

Properties of LCM 460 and 467

(i) The LCM of 467 and 460 is associative

LCM of 460 and 467 = LCM of 467 and 460

Related Least Common Multiples of 460

Related Least Common Multiples of 467

Frequently Asked Questions on LCM of 460 and 467

1. What is the LCM of 460 and 467?

Answer: LCM of 460 and 467 is 214820.

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 467?

Answer: Factors of 467 are 1, 467. There are 2 integers that are factors of 467. The greatest factor of 467 is 467.

4. How to Find the LCM of 460 and 467?

Answer:

Least Common Multiple of 460 and 467 = 214820

Step 1: Find the prime factorization of 460

460 = 2 x 2 x 5 x 23

Step 2: Find the prime factorization of 467

467 = 467

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

LCM = 214820 = 2 x 2 x 5 x 23 x 467

Step 4: Therefore, the least common multiple of 460 and 467 is 214820.