Least Common Multiple of 51 and 59

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

• Least Common Multiple of 51 and 59 by Prime method
• Least Common Multiple of 51 and 59 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 51 and 59. First we will calculate the prime factors of 51 and 59.

Prime Factorization of 51

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

51 = 3¹×17¹

Prime Factorization of 59

Prime factors of 59 are 59. Prime factorization of 59 in exponential form is:

59 = 59¹

Now multiplying the highest exponent prime factors to calculate the LCM of 51 and 59.

LCM(51,59) = 3¹×17¹×59¹
LCM(51,59) = 3009

Factors of 51

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

1, 3, 17, 51

Factors of 59

List of positive integer factors of 59 that divides 59 without a remainder.

1, 59

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51 and 59, than apply into the LCM equation.

GCF(51,59) = 1
LCM(51,59) = ( 51 × 59) / 1
LCM(51,59) = 3009 / 1
LCM(51,59) = 3009

(i) The LCM of 59 and 51 is associative

LCM of 51 and 59 = LCM of 59 and 51

1. What is the LCM of 51 and 59?

Answer: LCM of 51 and 59 is 3009.

2. 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.

3. What are the Factors of 59?

Answer: Factors of 59 are 1, 59. There are 2 integers that are factors of 59. The greatest factor of 59 is 59.

4. How to Find the LCM of 51 and 59?

Answer:

Least Common Multiple of 51 and 59 = 3009

Step 1: Find the prime factorization of 51

51 = 3 x 17

Step 2: Find the prime factorization of 59

59 = 59

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

LCM = 3009 = 3 x 17 x 59

Step 4: Therefore, the least common multiple of 51 and 59 is 3009.