Least Common Multiple of 459 and 464

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 464 the smallest integer that is 212976 that is divisible by both numbers.

Least Common Multiple (LCM) of 459 and 464 is 212976.

LCM(459,464) = 212976

LCM of 459 and 464

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

LCM of:
and

Least Common Multiple of 459 and 464

LCM of 459 and 464 is 212976

Least common multiple can be found by multiplying the highest exponent prime factors of 459 and 464. First we will calculate the prime factors of 459 and 464.

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 464


2 464
2 232
2 116
2 58
29 29
1

Prime factors of 464 are 2,29. Prime factorization of 464 in exponential form is:

464 = 24×291

Now multiplying the highest exponent prime factors to calculate the LCM of 459 and 464.

LCM(459,464) = 24×33×171×291
LCM(459,464) = 212976

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 464

List of positive integer factors of 464 that divides 464 without a remainder.

1, 2, 4, 8, 16, 29, 58, 116, 232, 464

Least Common Multiple of 459 and 464 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 464, than apply into the LCM equation.

GCF(459,464) = 1
LCM(459,464) = ( 459 × 464) / 1
LCM(459,464) = 212976 / 1
LCM(459,464) = 212976

Properties of LCM 459 and 464

(i) The LCM of 464 and 459 is associative

LCM of 459 and 464 = LCM of 464 and 459

Related Least Common Multiples of 459

Related Least Common Multiples of 464

Frequently Asked Questions on LCM of 459 and 464

1. What is the LCM of 459 and 464?

Answer: LCM of 459 and 464 is 212976.

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 464?

Answer: Factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, 464. There are 10 integers that are factors of 464. The greatest factor of 464 is 464.

4. How to Find the LCM of 459 and 464?

Answer:

Least Common Multiple of 459 and 464 = 212976

Step 1: Find the prime factorization of 459

459 = 3 x 3 x 3 x 17

Step 2: Find the prime factorization of 464

464 = 2 x 2 x 2 x 2 x 29

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

LCM = 212976 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 17 x 29

Step 4: Therefore, the least common multiple of 459 and 464 is 212976.