Least Common Multiple of 49 and 53

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

• Least Common Multiple of 49 and 53 by Prime method
• Least Common Multiple of 49 and 53 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 53. First we will calculate the prime factors of 49 and 53.

Prime Factorization of 49

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

49 = 7²

Prime Factorization of 53

Prime factors of 53 are 53. Prime factorization of 53 in exponential form is:

53 = 53¹

Now multiplying the highest exponent prime factors to calculate the LCM of 49 and 53.

LCM(49,53) = 7²×53¹
LCM(49,53) = 2597

Factors of 49

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

1, 7, 49

Factors of 53

List of positive integer factors of 53 that divides 53 without a remainder.

1, 53

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 53, than apply into the LCM equation.

GCF(49,53) = 1
LCM(49,53) = ( 49 × 53) / 1
LCM(49,53) = 2597 / 1
LCM(49,53) = 2597

(i) The LCM of 53 and 49 is associative

LCM of 49 and 53 = LCM of 53 and 49

1. What is the LCM of 49 and 53?

Answer: LCM of 49 and 53 is 2597.

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 53?

Answer: Factors of 53 are 1, 53. There are 2 integers that are factors of 53. The greatest factor of 53 is 53.

4. How to Find the LCM of 49 and 53?

Answer:

Least Common Multiple of 49 and 53 = 2597

Step 1: Find the prime factorization of 49

49 = 7 x 7

Step 2: Find the prime factorization of 53

53 = 53

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

LCM = 2597 = 7 x 7 x 53

Step 4: Therefore, the least common multiple of 49 and 53 is 2597.