Least Common Multiple of 49 and 57

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

• Least Common Multiple of 49 and 57 by Prime method
• Least Common Multiple of 49 and 57 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 57. First we will calculate the prime factors of 49 and 57.

Prime Factorization of 49

Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:

49 = 7²

Prime Factorization of 57

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

57 = 3¹×19¹

Now multiplying the highest exponent prime factors to calculate the LCM of 49 and 57.

LCM(49,57) = 3¹×7²×19¹
LCM(49,57) = 2793

Factors of 49

List of positive integer factors of 49 that divides 49 without a remainder.

1, 7, 49

Factors of 57

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

1, 3, 19, 57

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 57, than apply into the LCM equation.

GCF(49,57) = 1
LCM(49,57) = ( 49 × 57) / 1
LCM(49,57) = 2793 / 1
LCM(49,57) = 2793

(i) The LCM of 57 and 49 is associative

LCM of 49 and 57 = LCM of 57 and 49

1. What is the LCM of 49 and 57?

Answer: LCM of 49 and 57 is 2793.

2. What are the Factors of 49?

Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.

3. 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.

4. How to Find the LCM of 49 and 57?

Answer:

Least Common Multiple of 49 and 57 = 2793

Step 1: Find the prime factorization of 49

49 = 7 x 7

Step 2: Find the prime factorization of 57

57 = 3 x 19

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

LCM = 2793 = 3 x 7 x 7 x 19

Step 4: Therefore, the least common multiple of 49 and 57 is 2793.