Least Common Multiple of 420 and 425

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 425 the smallest integer that is 35700 that is divisible by both numbers.

Least Common Multiple (LCM) of 420 and 425 is 35700.

LCM(420,425) = 35700

LCM of 420 and 425

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

LCM of:
and

Least Common Multiple of 420 and 425

LCM of 420 and 425 is 35700

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 425. First we will calculate the prime factors of 420 and 425.

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 425


5 425
5 85
17 17
1

Prime factors of 425 are 5,17. Prime factorization of 425 in exponential form is:

425 = 52×171

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 425.

LCM(420,425) = 22×31×52×71×171
LCM(420,425) = 35700

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 425

List of positive integer factors of 425 that divides 425 without a remainder.

1, 5, 17, 25, 85, 425

Least Common Multiple of 420 and 425 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 425, than apply into the LCM equation.

GCF(420,425) = 5
LCM(420,425) = ( 420 × 425) / 5
LCM(420,425) = 178500 / 5
LCM(420,425) = 35700

Properties of LCM 420 and 425

(i) The LCM of 425 and 420 is associative

LCM of 420 and 425 = LCM of 425 and 420

Related Least Common Multiples of 420

Related Least Common Multiples of 425

Frequently Asked Questions on LCM of 420 and 425

1. What is the LCM of 420 and 425?

Answer: LCM of 420 and 425 is 35700.

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 425?

Answer: Factors of 425 are 1, 5, 17, 25, 85, 425. There are 6 integers that are factors of 425. The greatest factor of 425 is 425.

4. How to Find the LCM of 420 and 425?

Answer:

Least Common Multiple of 420 and 425 = 35700

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 425

425 = 5 x 5 x 17

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

LCM = 35700 = 2 x 2 x 3 x 5 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 420 and 425 is 35700.