Least Common Multiple of 420 and 421

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 421 the smallest integer that is 176820 that is divisible by both numbers.

Least Common Multiple (LCM) of 420 and 421 is 176820.

LCM(420,421) = 176820

LCM of 420 and 421

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

LCM of:
and

Least Common Multiple of 420 and 421

LCM of 420 and 421 is 176820

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 421. First we will calculate the prime factors of 420 and 421.

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 421


421 421
1

Prime factors of 421 are 421. Prime factorization of 421 in exponential form is:

421 = 4211

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 421.

LCM(420,421) = 22×31×51×71×4211
LCM(420,421) = 176820

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 421

List of positive integer factors of 421 that divides 421 without a remainder.

1, 421

Least Common Multiple of 420 and 421 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 421, than apply into the LCM equation.

GCF(420,421) = 1
LCM(420,421) = ( 420 × 421) / 1
LCM(420,421) = 176820 / 1
LCM(420,421) = 176820

Properties of LCM 420 and 421

(i) The LCM of 421 and 420 is associative

LCM of 420 and 421 = LCM of 421 and 420

Related Least Common Multiples of 420

Related Least Common Multiples of 421

Frequently Asked Questions on LCM of 420 and 421

1. What is the LCM of 420 and 421?

Answer: LCM of 420 and 421 is 176820.

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 421?

Answer: Factors of 421 are 1, 421. There are 2 integers that are factors of 421. The greatest factor of 421 is 421.

4. How to Find the LCM of 420 and 421?

Answer:

Least Common Multiple of 420 and 421 = 176820

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 421

421 = 421

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

LCM = 176820 = 2 x 2 x 3 x 5 x 7 x 421

Step 4: Therefore, the least common multiple of 420 and 421 is 176820.