Least Common Multiple of 459 and 462

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 462 the smallest integer that is 70686 that is divisible by both numbers.

Least Common Multiple (LCM) of 459 and 462 is 70686.

LCM(459,462) = 70686

LCM of 459 and 462

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

LCM of:
and

Least Common Multiple of 459 and 462

LCM of 459 and 462 is 70686

Least common multiple can be found by multiplying the highest exponent prime factors of 459 and 462. First we will calculate the prime factors of 459 and 462.

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 462


2 462
3 231
7 77
11 11
1

Prime factors of 462 are 2, 3, 7,11. Prime factorization of 462 in exponential form is:

462 = 21×31×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 459 and 462.

LCM(459,462) = 21×33×71×111×171
LCM(459,462) = 70686

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 462

List of positive integer factors of 462 that divides 462 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462

Least Common Multiple of 459 and 462 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 462, than apply into the LCM equation.

GCF(459,462) = 3
LCM(459,462) = ( 459 × 462) / 3
LCM(459,462) = 212058 / 3
LCM(459,462) = 70686

Properties of LCM 459 and 462

(i) The LCM of 462 and 459 is associative

LCM of 459 and 462 = LCM of 462 and 459

Related Least Common Multiples of 459

Related Least Common Multiples of 462

Frequently Asked Questions on LCM of 459 and 462

1. What is the LCM of 459 and 462?

Answer: LCM of 459 and 462 is 70686.

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 462?

Answer: Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462. There are 16 integers that are factors of 462. The greatest factor of 462 is 462.

4. How to Find the LCM of 459 and 462?

Answer:

Least Common Multiple of 459 and 462 = 70686

Step 1: Find the prime factorization of 459

459 = 3 x 3 x 3 x 17

Step 2: Find the prime factorization of 462

462 = 2 x 3 x 7 x 11

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

LCM = 70686 = 2 x 3 x 3 x 3 x 7 x 11 x 17

Step 4: Therefore, the least common multiple of 459 and 462 is 70686.