Least Common Multiple of 10 and 21

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

• Least Common Multiple of 10 and 21 by Prime method
• Least Common Multiple of 10 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 21. First we will calculate the prime factors of 10 and 21.

Prime Factorization of 10

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 2¹×5¹

Prime Factorization of 21

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 3¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 21.

LCM(10,21) = 2¹×3¹×5¹×7¹
LCM(10,21) = 210

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 21, than apply into the LCM equation.

GCF(10,21) = 1
LCM(10,21) = ( 10 × 21) / 1
LCM(10,21) = 210 / 1
LCM(10,21) = 210

(i) The LCM of 21 and 10 is associative

LCM of 10 and 21 = LCM of 21 and 10

1. What is the LCM of 10 and 21?

Answer: LCM of 10 and 21 is 210.

2. What are the Factors of 10?

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

3. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 10 and 21?

Answer:

Least Common Multiple of 10 and 21 = 210

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 21

21 = 3 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 = 210 = 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 10 and 21 is 210.