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Least Common Multiple of 7 and 21

Free LCM Calculator determines the least common multiple (LCM) between 7 and 21 the smallest integer that is 21 that is divisible by both numbers.

Least Common Multiple (LCM) of 7 and 21 is 21.

LCM(7,21) = 21

LCM of 7 and 21

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

LCM of:
and

Least Common Multiple (LCM) of 7 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 21. First we will calculate the prime factors of 7 and 21.

Prime Factorization of 7


7 7
1

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

7 = 71

Prime Factorization of 21


3 21
7 7
1

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 7 and 21.

LCM(7,21) = 31×71
LCM(7,21) = 21

Factors of 7

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

1, 7

Factors of 21

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

1, 3, 7, 21

Least Common Multiple of 7 and 21 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 21, than apply into the LCM equation.

GCF(7,21) = 7
LCM(7,21) = ( 7 × 21) / 7
LCM(7,21) = 147 / 7
LCM(7,21) = 21

Least Common Multiple of 7 and 21 by Listing Multiples

Multiples of 7

7, 14,21

Multiples of 21

21

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 7 and 21 is 21

Properties of LCM 7 and 21

(i) The LCM of 21 and 7 is associative

LCM of 7 and 21 = LCM of 21 and 7

Frequently Asked Questions on LCM of 7 and 21

1. What is the LCM of 7 and 21?

Answer: LCM of 7 and 21 is 21.

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 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 7 and 21?

Answer:

Least Common Multiple of 7 and 21 = 21

Step 1: Find the prime factorization of 7

7 = 7

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 = 21 = 3 x 7

Step 4: Therefore, the least common multiple of 7 and 21 is 21.