Least Common Multiple of 57 and 61

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

• Least Common Multiple of 57 and 61 by Prime method
• Least Common Multiple of 57 and 61 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 57 and 61. First we will calculate the prime factors of 57 and 61.

Prime Factorization of 57

Prime factors of 57 are 3,19. Prime factorization of 57 in exponential form is:

57 = 3¹×19¹

Prime Factorization of 61

Prime factors of 61 are 61. Prime factorization of 61 in exponential form is:

61 = 61¹

Now multiplying the highest exponent prime factors to calculate the LCM of 57 and 61.

LCM(57,61) = 3¹×19¹×61¹
LCM(57,61) = 3477

Factors of 57

List of positive integer factors of 57 that divides 57 without a remainder.

1, 3, 19, 57

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1, 61

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57 and 61, than apply into the LCM equation.

GCF(57,61) = 1
LCM(57,61) = ( 57 × 61) / 1
LCM(57,61) = 3477 / 1
LCM(57,61) = 3477

(i) The LCM of 61 and 57 is associative

LCM of 57 and 61 = LCM of 61 and 57

1. What is the LCM of 57 and 61?

Answer: LCM of 57 and 61 is 3477.

2. What are the Factors of 57?

Answer: Factors of 57 are 1, 3, 19, 57. There are 4 integers that are factors of 57. The greatest factor of 57 is 57.

3. What are the Factors of 61?

Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.

4. How to Find the LCM of 57 and 61?

Answer:

Least Common Multiple of 57 and 61 = 3477

Step 1: Find the prime factorization of 57

57 = 3 x 19

Step 2: Find the prime factorization of 61

61 = 61

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

LCM = 3477 = 3 x 19 x 61

Step 4: Therefore, the least common multiple of 57 and 61 is 3477.