Least Common Multiple of 77 and 83

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

• Least Common Multiple of 77 and 83 by Prime method
• Least Common Multiple of 77 and 83 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 77 and 83. First we will calculate the prime factors of 77 and 83.

Prime Factorization of 77

Prime factors of 77 are 7,11. Prime factorization of 77 in exponential form is:

77 = 7¹×11¹

Prime Factorization of 83

Prime factors of 83 are 83. Prime factorization of 83 in exponential form is:

83 = 83¹

Now multiplying the highest exponent prime factors to calculate the LCM of 77 and 83.

LCM(77,83) = 7¹×11¹×83¹
LCM(77,83) = 6391

Factors of 77

List of positive integer factors of 77 that divides 77 without a remainder.

1, 7, 11, 77

Factors of 83

List of positive integer factors of 83 that divides 83 without a remainder.

1, 83

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77 and 83, than apply into the LCM equation.

GCF(77,83) = 1
LCM(77,83) = ( 77 × 83) / 1
LCM(77,83) = 6391 / 1
LCM(77,83) = 6391

(i) The LCM of 83 and 77 is associative

LCM of 77 and 83 = LCM of 83 and 77

1. What is the LCM of 77 and 83?

Answer: LCM of 77 and 83 is 6391.

2. What are the Factors of 77?

Answer: Factors of 77 are 1, 7, 11, 77. There are 4 integers that are factors of 77. The greatest factor of 77 is 77.

3. What are the Factors of 83?

Answer: Factors of 83 are 1, 83. There are 2 integers that are factors of 83. The greatest factor of 83 is 83.

4. How to Find the LCM of 77 and 83?

Answer:

Least Common Multiple of 77 and 83 = 6391

Step 1: Find the prime factorization of 77

77 = 7 x 11

Step 2: Find the prime factorization of 83

83 = 83

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

LCM = 6391 = 7 x 11 x 83

Step 4: Therefore, the least common multiple of 77 and 83 is 6391.