Least Common Multiple of 420 and 424

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 420 and 424 the smallest integer that is 44520 that is divisible by both numbers.

Least Common Multiple (LCM) of 420 and 424 is 44520.

LCM(420,424) = 44520

LCM of 420 and 424

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

LCM of:
and

Least Common Multiple of 420 and 424

LCM of 420 and 424 is 44520

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 424. First we will calculate the prime factors of 420 and 424.

Prime Factorization of 420


2 420
2 210
3 105
5 35
7 7
1

Prime factors of 420 are 2, 3, 5,7. Prime factorization of 420 in exponential form is:

420 = 22×31×51×71

Prime Factorization of 424


2 424
2 212
2 106
53 53
1

Prime factors of 424 are 2,53. Prime factorization of 424 in exponential form is:

424 = 23×531

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 424.

LCM(420,424) = 23×31×51×71×531
LCM(420,424) = 44520

Factors of 420

List of positive integer factors of 420 that divides 420 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

Factors of 424

List of positive integer factors of 424 that divides 424 without a remainder.

1, 2, 4, 8, 53, 106, 212, 424

Least Common Multiple of 420 and 424 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 424, than apply into the LCM equation.

GCF(420,424) = 4
LCM(420,424) = ( 420 × 424) / 4
LCM(420,424) = 178080 / 4
LCM(420,424) = 44520

Properties of LCM 420 and 424

(i) The LCM of 424 and 420 is associative

LCM of 420 and 424 = LCM of 424 and 420

Related Least Common Multiples of 420

Related Least Common Multiples of 424

Frequently Asked Questions on LCM of 420 and 424

1. What is the LCM of 420 and 424?

Answer: LCM of 420 and 424 is 44520.

2. What are the Factors of 420?

Answer: Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. There are 24 integers that are factors of 420. The greatest factor of 420 is 420.

3. What are the Factors of 424?

Answer: Factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424. There are 8 integers that are factors of 424. The greatest factor of 424 is 424.

4. How to Find the LCM of 420 and 424?

Answer:

Least Common Multiple of 420 and 424 = 44520

Step 1: Find the prime factorization of 420

420 = 2 x 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 424

424 = 2 x 2 x 2 x 53

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

LCM = 44520 = 2 x 2 x 2 x 3 x 5 x 7 x 53

Step 4: Therefore, the least common multiple of 420 and 424 is 44520.