Least Common Multiple of 49 and 51

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

• Least Common Multiple of 49 and 51 by Prime method
• Least Common Multiple of 49 and 51 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 51. First we will calculate the prime factors of 49 and 51.

Prime Factorization of 49

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

49 = 7²

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 49 and 51.

LCM(49,51) = 3¹×7²×17¹
LCM(49,51) = 2499

Factors of 49

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

1, 7, 49

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 49 and 51, than apply into the LCM equation.

GCF(49,51) = 1
LCM(49,51) = ( 49 × 51) / 1
LCM(49,51) = 2499 / 1
LCM(49,51) = 2499

(i) The LCM of 51 and 49 is associative

LCM of 49 and 51 = LCM of 51 and 49

1. What is the LCM of 49 and 51?

Answer: LCM of 49 and 51 is 2499.

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 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 49 and 51?

Answer:

Least Common Multiple of 49 and 51 = 2499

Step 1: Find the prime factorization of 49

49 = 7 x 7

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 = 2499 = 3 x 7 x 7 x 17

Step 4: Therefore, the least common multiple of 49 and 51 is 2499.