Least Common Multiple of 21 and 35

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

• Least Common Multiple of 21 and 35 by Prime method
• Least Common Multiple of 21 and 35 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 35. First we will calculate the prime factors of 21 and 35.

Prime Factorization of 21

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

21 = 3¹×7¹

Prime Factorization of 35

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 21 and 35.

LCM(21,35) = 3¹×5¹×7¹
LCM(21,35) = 105

Factors of 21

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

1, 3, 7, 21

Factors of 35

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

1, 5, 7, 35

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21 and 35, than apply into the LCM equation.

GCF(21,35) = 7
LCM(21,35) = ( 21 × 35) / 7
LCM(21,35) = 735 / 7
LCM(21,35) = 105

(i) The LCM of 35 and 21 is associative

LCM of 21 and 35 = LCM of 35 and 21

1. What is the LCM of 21 and 35?

Answer: LCM of 21 and 35 is 105.

2. 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.

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 21 and 35?

Answer:

Least Common Multiple of 21 and 35 = 105

Step 1: Find the prime factorization of 21

21 = 3 x 7

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 = 105 = 3 x 5 x 7

Step 4: Therefore, the least common multiple of 21 and 35 is 105.