Least Common Multiple of 49 and 69

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

• Least Common Multiple of 49 and 69 by Prime method
• Least Common Multiple of 49 and 69 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 49 and 69. First we will calculate the prime factors of 49 and 69.

Prime Factorization of 49

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

49 = 7²

Prime Factorization of 69

Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:

69 = 3¹×23¹

Now multiplying the highest exponent prime factors to calculate the LCM of 49 and 69.

LCM(49,69) = 3¹×7²×23¹
LCM(49,69) = 3381

Factors of 49

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

1, 7, 49

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1, 3, 23, 69

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49 and 69, than apply into the LCM equation.

GCF(49,69) = 1
LCM(49,69) = ( 49 × 69) / 1
LCM(49,69) = 3381 / 1
LCM(49,69) = 3381

(i) The LCM of 69 and 49 is associative

LCM of 49 and 69 = LCM of 69 and 49

1. What is the LCM of 49 and 69?

Answer: LCM of 49 and 69 is 3381.

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 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

4. How to Find the LCM of 49 and 69?

Answer:

Least Common Multiple of 49 and 69 = 3381

Step 1: Find the prime factorization of 49

49 = 7 x 7

Step 2: Find the prime factorization of 69

69 = 3 x 23

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

LCM = 3381 = 3 x 7 x 7 x 23

Step 4: Therefore, the least common multiple of 49 and 69 is 3381.