Least Common Multiple of 420 and 428

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 428 the smallest integer that is 44940 that is divisible by both numbers.

Least Common Multiple (LCM) of 420 and 428 is 44940.

LCM(420,428) = 44940

LCM of 420 and 428

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

LCM of:
and

Least Common Multiple of 420 and 428

LCM of 420 and 428 is 44940

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 428. First we will calculate the prime factors of 420 and 428.

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 428


2 428
2 214
107 107
1

Prime factors of 428 are 2,107. Prime factorization of 428 in exponential form is:

428 = 22×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 428.

LCM(420,428) = 22×31×51×71×1071
LCM(420,428) = 44940

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 428

List of positive integer factors of 428 that divides 428 without a remainder.

1, 2, 4, 107, 214, 428

Least Common Multiple of 420 and 428 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 428, than apply into the LCM equation.

GCF(420,428) = 4
LCM(420,428) = ( 420 × 428) / 4
LCM(420,428) = 179760 / 4
LCM(420,428) = 44940

Properties of LCM 420 and 428

(i) The LCM of 428 and 420 is associative

LCM of 420 and 428 = LCM of 428 and 420

Related Least Common Multiples of 420

Related Least Common Multiples of 428

Frequently Asked Questions on LCM of 420 and 428

1. What is the LCM of 420 and 428?

Answer: LCM of 420 and 428 is 44940.

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 428?

Answer: Factors of 428 are 1, 2, 4, 107, 214, 428. There are 6 integers that are factors of 428. The greatest factor of 428 is 428.

4. How to Find the LCM of 420 and 428?

Answer:

Least Common Multiple of 420 and 428 = 44940

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 428

428 = 2 x 2 x 107

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

LCM = 44940 = 2 x 2 x 3 x 5 x 7 x 107

Step 4: Therefore, the least common multiple of 420 and 428 is 44940.