Least Common Multiple of 49 and 55

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

• Least Common Multiple of 49 and 55 by Prime method
• Least Common Multiple of 49 and 55 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 55. First we will calculate the prime factors of 49 and 55.

Prime Factorization of 49

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

49 = 7²

Prime Factorization of 55

Prime factors of 55 are 5,11. Prime factorization of 55 in exponential form is:

55 = 5¹×11¹

Now multiplying the highest exponent prime factors to calculate the LCM of 49 and 55.

LCM(49,55) = 5¹×7²×11¹
LCM(49,55) = 2695

Factors of 49

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

1, 7, 49

Factors of 55

List of positive integer factors of 55 that divides 55 without a remainder.

1, 5, 11, 55

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 55, than apply into the LCM equation.

GCF(49,55) = 1
LCM(49,55) = ( 49 × 55) / 1
LCM(49,55) = 2695 / 1
LCM(49,55) = 2695

(i) The LCM of 55 and 49 is associative

LCM of 49 and 55 = LCM of 55 and 49

1. What is the LCM of 49 and 55?

Answer: LCM of 49 and 55 is 2695.

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 55?

Answer: Factors of 55 are 1, 5, 11, 55. There are 4 integers that are factors of 55. The greatest factor of 55 is 55.

4. How to Find the LCM of 49 and 55?

Answer:

Least Common Multiple of 49 and 55 = 2695

Step 1: Find the prime factorization of 49

49 = 7 x 7

Step 2: Find the prime factorization of 55

55 = 5 x 11

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

LCM = 2695 = 5 x 7 x 7 x 11

Step 4: Therefore, the least common multiple of 49 and 55 is 2695.