Least Common Multiple of 47 and 51

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

• Least Common Multiple of 47 and 51 by Prime method
• Least Common Multiple of 47 and 51 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 47 and 51. First we will calculate the prime factors of 47 and 51.

Prime Factorization of 47

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

47 = 47¹

Prime Factorization of 51

Prime factors of 51 are 3,17. Prime factorization of 51 in exponential form is:

51 = 3¹×17¹

Now multiplying the highest exponent prime factors to calculate the LCM of 47 and 51.

LCM(47,51) = 3¹×17¹×47¹
LCM(47,51) = 2397

Factors of 47

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

1, 47

Factors of 51

List of positive integer factors of 51 that divides 51 without a remainder.

1, 3, 17, 51

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 47 and 51, than apply into the LCM equation.

GCF(47,51) = 1
LCM(47,51) = ( 47 × 51) / 1
LCM(47,51) = 2397 / 1
LCM(47,51) = 2397

(i) The LCM of 51 and 47 is associative

LCM of 47 and 51 = LCM of 51 and 47

1. What is the LCM of 47 and 51?

Answer: LCM of 47 and 51 is 2397.

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 51?

Answer: Factors of 51 are 1, 3, 17, 51. There are 4 integers that are factors of 51. The greatest factor of 51 is 51.

4. How to Find the LCM of 47 and 51?

Answer:

Least Common Multiple of 47 and 51 = 2397

Step 1: Find the prime factorization of 47

47 = 47

Step 2: Find the prime factorization of 51

51 = 3 x 17

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

LCM = 2397 = 3 x 17 x 47

Step 4: Therefore, the least common multiple of 47 and 51 is 2397.