Least Common Multiple of 459 and 465

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 459 and 465 the smallest integer that is 71145 that is divisible by both numbers.

Least Common Multiple (LCM) of 459 and 465 is 71145.

LCM(459,465) = 71145

LCM of 459 and 465

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

LCM of:
and

Least Common Multiple of 459 and 465

LCM of 459 and 465 is 71145

Least common multiple can be found by multiplying the highest exponent prime factors of 459 and 465. First we will calculate the prime factors of 459 and 465.

Prime Factorization of 459


3 459
3 153
3 51
17 17
1

Prime factors of 459 are 3,17. Prime factorization of 459 in exponential form is:

459 = 33×171

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

Now multiplying the highest exponent prime factors to calculate the LCM of 459 and 465.

LCM(459,465) = 33×51×171×311
LCM(459,465) = 71145

Factors of 459

List of positive integer factors of 459 that divides 459 without a remainder.

1, 3, 9, 17, 27, 51, 153, 459

Factors of 465

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

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

Least Common Multiple of 459 and 465 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 459 and 465, than apply into the LCM equation.

GCF(459,465) = 3
LCM(459,465) = ( 459 × 465) / 3
LCM(459,465) = 213435 / 3
LCM(459,465) = 71145

Properties of LCM 459 and 465

(i) The LCM of 465 and 459 is associative

LCM of 459 and 465 = LCM of 465 and 459

Related Least Common Multiples of 459

Related Least Common Multiples of 465

Frequently Asked Questions on LCM of 459 and 465

1. What is the LCM of 459 and 465?

Answer: LCM of 459 and 465 is 71145.

2. What are the Factors of 459?

Answer: Factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459. There are 8 integers that are factors of 459. The greatest factor of 459 is 459.

3. 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.

4. How to Find the LCM of 459 and 465?

Answer:

Least Common Multiple of 459 and 465 = 71145

Step 1: Find the prime factorization of 459

459 = 3 x 3 x 3 x 17

Step 2: Find the prime factorization of 465

465 = 3 x 5 x 31

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

LCM = 71145 = 3 x 3 x 3 x 5 x 17 x 31

Step 4: Therefore, the least common multiple of 459 and 465 is 71145.