Least Common Multiple of 30 and 47

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023


Free LCM Calculator determines the least common multiple (LCM) between 30 and 47 the smallest integer that is 1410 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 47 is 1410.

LCM(30,47) = 1410

LCM of 30 and 47

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

LCM of:
and

Least Common Multiple of 30 and 47

LCM of 30 and 47 is 1410

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 47. First we will calculate the prime factors of 30 and 47.

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

Prime Factorization of 47


47 47
1

Prime factors of 47 are 47. Prime factorization of 47 in exponential form is:

47 = 471

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 47.

LCM(30,47) = 21×31×51×471
LCM(30,47) = 1410

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

Factors of 47

List of positive integer factors of 47 that divides 47 without a remainder.

1, 47

Least Common Multiple of 30 and 47 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 47, than apply into the LCM equation.

GCF(30,47) = 1
LCM(30,47) = ( 30 × 47) / 1
LCM(30,47) = 1410 / 1
LCM(30,47) = 1410

Properties of LCM 30 and 47

(i) The LCM of 47 and 30 is associative

LCM of 30 and 47 = LCM of 47 and 30

Frequently Asked Questions on LCM of 30 and 47

1. What is the LCM of 30 and 47?

Answer: LCM of 30 and 47 is 1410.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

3. What are the Factors of 47?

Answer: Factors of 47 are 1, 47. There are 2 integers that are factors of 47. The greatest factor of 47 is 47.

4. How to Find the LCM of 30 and 47?

Answer:

Least Common Multiple of 30 and 47 = 1410

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 47

47 = 47

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 1410 = 2 x 3 x 5 x 47

Step 4: Therefore, the least common multiple of 30 and 47 is 1410.