Least Common Multiple of 47 and 6

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

• Least Common Multiple of 47 and 6 by Prime method
• Least Common Multiple of 47 and 6 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 47 and 6. First we will calculate the prime factors of 47 and 6.

Prime Factorization of 47

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

47 = 47¹

Prime Factorization of 6

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 2¹×3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 47 and 6.

LCM(47,6) = 2¹×3¹×47¹
LCM(47,6) = 282

Factors of 47

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

1, 47

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3, 6

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 47 and 6, than apply into the LCM equation.

GCF(47,6) = 1
LCM(47,6) = ( 47 × 6) / 1
LCM(47,6) = 282 / 1
LCM(47,6) = 282

(i) The LCM of 6 and 47 is associative

LCM of 47 and 6 = LCM of 6 and 47

1. What is the LCM of 47 and 6?

Answer: LCM of 47 and 6 is 282.

2. 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.

3. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

4. How to Find the LCM of 47 and 6?

Answer:

Least Common Multiple of 47 and 6 = 282

Step 1: Find the prime factorization of 47

47 = 47

Step 2: Find the prime factorization of 6

6 = 2 x 3

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

LCM = 282 = 2 x 3 x 47

Step 4: Therefore, the least common multiple of 47 and 6 is 282.