Least Common Multiple of 7 and 20

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

• Least Common Multiple of 7 and 20 by Prime method
• Least Common Multiple of 7 and 20 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 20. First we will calculate the prime factors of 7 and 20.

Prime Factorization of 7

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

7 = 7¹

Prime Factorization of 20

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

20 = 2²×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 20.

LCM(7,20) = 2²×5¹×7¹
LCM(7,20) = 140

Factors of 7

List of positive integer factors of 7 that divides 7 without a remainder.

1, 7

Factors of 20

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

1, 2, 4, 5, 10, 20

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 20, than apply into the LCM equation.

GCF(7,20) = 1
LCM(7,20) = ( 7 × 20) / 1
LCM(7,20) = 140 / 1
LCM(7,20) = 140

(i) The LCM of 20 and 7 is associative

LCM of 7 and 20 = LCM of 20 and 7

1. What is the LCM of 7 and 20?

Answer: LCM of 7 and 20 is 140.

2. What are the Factors of 7?

Answer: Factors of 7 are 1, 7. There are 2 integers that are factors of 7. The greatest factor of 7 is 7.

3. 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.

4. How to Find the LCM of 7 and 20?

Answer:

Least Common Multiple of 7 and 20 = 140

Step 1: Find the prime factorization of 7

7 = 7

Step 2: Find the prime factorization of 20

20 = 2 x 2 x 5

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 7 and 20 is 140.