Least Common Multiple of 465 and 470

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 470 the smallest integer that is 43710 that is divisible by both numbers.

Least Common Multiple (LCM) of 465 and 470 is 43710.

LCM(465,470) = 43710

LCM of 465 and 470

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

LCM of:
and

Least Common Multiple of 465 and 470

LCM of 465 and 470 is 43710

Least common multiple can be found by multiplying the highest exponent prime factors of 465 and 470. First we will calculate the prime factors of 465 and 470.

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 470


2 470
5 235
47 47
1

Prime factors of 470 are 2, 5,47. Prime factorization of 470 in exponential form is:

470 = 21×51×471

Now multiplying the highest exponent prime factors to calculate the LCM of 465 and 470.

LCM(465,470) = 21×31×51×311×471
LCM(465,470) = 43710

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 470

List of positive integer factors of 470 that divides 470 without a remainder.

1, 2, 5, 10, 47, 94, 235, 470

Least Common Multiple of 465 and 470 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 470, than apply into the LCM equation.

GCF(465,470) = 5
LCM(465,470) = ( 465 × 470) / 5
LCM(465,470) = 218550 / 5
LCM(465,470) = 43710

Properties of LCM 465 and 470

(i) The LCM of 470 and 465 is associative

LCM of 465 and 470 = LCM of 470 and 465

Related Least Common Multiples of 465

Related Least Common Multiples of 470

Frequently Asked Questions on LCM of 465 and 470

1. What is the LCM of 465 and 470?

Answer: LCM of 465 and 470 is 43710.

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 470?

Answer: Factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470. There are 8 integers that are factors of 470. The greatest factor of 470 is 470.

4. How to Find the LCM of 465 and 470?

Answer:

Least Common Multiple of 465 and 470 = 43710

Step 1: Find the prime factorization of 465

465 = 3 x 5 x 31

Step 2: Find the prime factorization of 470

470 = 2 x 5 x 47

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

LCM = 43710 = 2 x 3 x 5 x 31 x 47

Step 4: Therefore, the least common multiple of 465 and 470 is 43710.