Least Common Multiple of 462 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 462 and 464 the smallest integer that is 107184 that is divisible by both numbers.

Least Common Multiple (LCM) of 462 and 464 is 107184.

LCM(462,464) = 107184

LCM of 462 and 464

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

LCM of:
and

Least Common Multiple of 462 and 464

LCM of 462 and 464 is 107184

Least common multiple can be found by multiplying the highest exponent prime factors of 462 and 464. First we will calculate the prime factors of 462 and 464.

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

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 462 and 464.

LCM(462,464) = 24×31×71×111×291
LCM(462,464) = 107184

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

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 462 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 462 and 464, than apply into the LCM equation.

GCF(462,464) = 2
LCM(462,464) = ( 462 × 464) / 2
LCM(462,464) = 214368 / 2
LCM(462,464) = 107184

Properties of LCM 462 and 464

(i) The LCM of 464 and 462 is associative

LCM of 462 and 464 = LCM of 464 and 462

Related Least Common Multiples of 462

Related Least Common Multiples of 464

Frequently Asked Questions on LCM of 462 and 464

1. What is the LCM of 462 and 464?

Answer: LCM of 462 and 464 is 107184.

2. 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.

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 462 and 464?

Answer:

Least Common Multiple of 462 and 464 = 107184

Step 1: Find the prime factorization of 462

462 = 2 x 3 x 7 x 11

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 = 107184 = 2 x 2 x 2 x 2 x 3 x 7 x 11 x 29

Step 4: Therefore, the least common multiple of 462 and 464 is 107184.