Least Common Multiple of 465 and 468

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 465 and 468 the smallest integer that is 72540 that is divisible by both numbers.

Least Common Multiple (LCM) of 465 and 468 is 72540.

LCM(465,468) = 72540

LCM of 465 and 468

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

LCM of:
and

Least Common Multiple of 465 and 468

LCM of 465 and 468 is 72540

Least common multiple can be found by multiplying the highest exponent prime factors of 465 and 468. First we will calculate the prime factors of 465 and 468.

Prime Factorization of 465


3 465
5 155
31 31
1

Prime factors of 465 are 3, 5,31. Prime factorization of 465 in exponential form is:

465 = 31×51×311

Prime Factorization of 468


2 468
2 234
3 117
3 39
13 13
1

Prime factors of 468 are 2, 3,13. Prime factorization of 468 in exponential form is:

468 = 22×32×131

Now multiplying the highest exponent prime factors to calculate the LCM of 465 and 468.

LCM(465,468) = 22×32×51×131×311
LCM(465,468) = 72540

Factors of 465

List of positive integer factors of 465 that divides 465 without a remainder.

1, 3, 5, 15, 31, 93, 155, 465

Factors of 468

List of positive integer factors of 468 that divides 468 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468

Least Common Multiple of 465 and 468 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 465 and 468, than apply into the LCM equation.

GCF(465,468) = 3
LCM(465,468) = ( 465 × 468) / 3
LCM(465,468) = 217620 / 3
LCM(465,468) = 72540

Properties of LCM 465 and 468

(i) The LCM of 468 and 465 is associative

LCM of 465 and 468 = LCM of 468 and 465

Related Least Common Multiples of 465

Related Least Common Multiples of 468

Frequently Asked Questions on LCM of 465 and 468

1. What is the LCM of 465 and 468?

Answer: LCM of 465 and 468 is 72540.

2. What are the Factors of 465?

Answer: Factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465. There are 8 integers that are factors of 465. The greatest factor of 465 is 465.

3. What are the Factors of 468?

Answer: Factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468. There are 18 integers that are factors of 468. The greatest factor of 468 is 468.

4. How to Find the LCM of 465 and 468?

Answer:

Least Common Multiple of 465 and 468 = 72540

Step 1: Find the prime factorization of 465

465 = 3 x 5 x 31

Step 2: Find the prime factorization of 468

468 = 2 x 2 x 3 x 3 x 13

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

LCM = 72540 = 2 x 2 x 3 x 3 x 5 x 13 x 31

Step 4: Therefore, the least common multiple of 465 and 468 is 72540.