Least Common Multiple of 465 and 472

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 472 the smallest integer that is 219480 that is divisible by both numbers.

Least Common Multiple (LCM) of 465 and 472 is 219480.

LCM(465,472) = 219480

LCM of 465 and 472

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

LCM of:
and

Least Common Multiple of 465 and 472

LCM of 465 and 472 is 219480

Least common multiple can be found by multiplying the highest exponent prime factors of 465 and 472. First we will calculate the prime factors of 465 and 472.

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 472


2 472
2 236
2 118
59 59
1

Prime factors of 472 are 2,59. Prime factorization of 472 in exponential form is:

472 = 23×591

Now multiplying the highest exponent prime factors to calculate the LCM of 465 and 472.

LCM(465,472) = 23×31×51×311×591
LCM(465,472) = 219480

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 472

List of positive integer factors of 472 that divides 472 without a remainder.

1, 2, 4, 8, 59, 118, 236, 472

Least Common Multiple of 465 and 472 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 472, than apply into the LCM equation.

GCF(465,472) = 1
LCM(465,472) = ( 465 × 472) / 1
LCM(465,472) = 219480 / 1
LCM(465,472) = 219480

Properties of LCM 465 and 472

(i) The LCM of 472 and 465 is associative

LCM of 465 and 472 = LCM of 472 and 465

Related Least Common Multiples of 465

Related Least Common Multiples of 472

Frequently Asked Questions on LCM of 465 and 472

1. What is the LCM of 465 and 472?

Answer: LCM of 465 and 472 is 219480.

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 472?

Answer: Factors of 472 are 1, 2, 4, 8, 59, 118, 236, 472. There are 8 integers that are factors of 472. The greatest factor of 472 is 472.

4. How to Find the LCM of 465 and 472?

Answer:

Least Common Multiple of 465 and 472 = 219480

Step 1: Find the prime factorization of 465

465 = 3 x 5 x 31

Step 2: Find the prime factorization of 472

472 = 2 x 2 x 2 x 59

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

LCM = 219480 = 2 x 2 x 2 x 3 x 5 x 31 x 59

Step 4: Therefore, the least common multiple of 465 and 472 is 219480.