Least Common Multiple of 20 and 35

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 20 and 35 the smallest integer that is 140 that is divisible by both numbers.

Least Common Multiple (LCM) of 20 and 35 is 140.

LCM(20,35) = 140

LCM of 20 and 35

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

LCM of:
and

Least Common Multiple of 20 and 35

LCM of 20 and 35 is 140

Least common multiple can be found by multiplying the highest exponent prime factors of 20 and 35. First we will calculate the prime factors of 20 and 35.

Prime Factorization of 20


2 20
2 10
5 5
1

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 22×51

Prime Factorization of 35


5 35
7 7
1

Prime factors of 35 are 5,7. Prime factorization of 35 in exponential form is:

35 = 51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 20 and 35.

LCM(20,35) = 22×51×71
LCM(20,35) = 140

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1, 5, 7, 35

Least Common Multiple of 20 and 35 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20 and 35, than apply into the LCM equation.

GCF(20,35) = 5
LCM(20,35) = ( 20 × 35) / 5
LCM(20,35) = 700 / 5
LCM(20,35) = 140

Properties of LCM 20 and 35

(i) The LCM of 35 and 20 is associative

LCM of 20 and 35 = LCM of 35 and 20

Frequently Asked Questions on LCM of 20 and 35

1. What is the LCM of 20 and 35?

Answer: LCM of 20 and 35 is 140.

2. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

3. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

4. How to Find the LCM of 20 and 35?

Answer:

Least Common Multiple of 20 and 35 = 140

Step 1: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 2: Find the prime factorization of 35

35 = 5 x 7

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

LCM = 140 = 2 x 2 x 5 x 7

Step 4: Therefore, the least common multiple of 20 and 35 is 140.