Euclid's Division Lemma Prime Factorisation Calculator Factors of a Number Calculator LCM Calculator GCF Calculator Factor Tree Calculator LCM of Decimals LCM of Fractions GCF of Decimals GCF of Fractions

Least Common Multiple of 3 and 7

Free LCM Calculator determines the least common multiple (LCM) between 3 and 7 the smallest integer that is 21 that is divisible by both numbers.

Least Common Multiple (LCM) of 3 and 7 is 21.

LCM(3,7) = 21

LCM of 3 and 7

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

LCM of:
and

Least Common Multiple (LCM) of 3 and 7 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 7. First we will calculate the prime factors of 3 and 7.

Prime Factorization of 3


3 3
1

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

3 = 31

Prime Factorization of 7


7 7
1

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

7 = 71

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 7.

LCM(3,7) = 31×71
LCM(3,7) = 21

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

Factors of 7

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

1, 7

Least Common Multiple of 3 and 7 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 7, than apply into the LCM equation.

GCF(3,7) = 1
LCM(3,7) = ( 3 × 7) / 1
LCM(3,7) = 21 / 1
LCM(3,7) = 21

Least Common Multiple of 3 and 7 by Listing Multiples

Multiples of 3

3, 6, 9, 12, 15, 18,21

Multiples of 7

7, 14,21

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

∴ Least Common Multiple of 3 and 7 is 21

Properties of LCM 3 and 7

(i) The LCM of 7 and 3 is associative

LCM of 3 and 7 = LCM of 7 and 3

Frequently Asked Questions on LCM of 3 and 7

1. What is the LCM of 3 and 7?

Answer: LCM of 3 and 7 is 21.

2. What are the Factors of 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

3. 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.

4. How to Find the LCM of 3 and 7?

Answer:

Least Common Multiple of 3 and 7 = 21

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 7

7 = 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 3 and 7 is 21.