Least Common Multiple of 71 and 77

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

• Least Common Multiple of 71 and 77 by Prime method
• Least Common Multiple of 71 and 77 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 71 and 77. First we will calculate the prime factors of 71 and 77.

Prime Factorization of 71

Prime factors of 71 are 71. Prime factorization of 71 in exponential form is:

71 = 71¹

Prime Factorization of 77

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

77 = 7¹×11¹

Now multiplying the highest exponent prime factors to calculate the LCM of 71 and 77.

LCM(71,77) = 7¹×11¹×71¹
LCM(71,77) = 5467

Factors of 71

List of positive integer factors of 71 that divides 71 without a remainder.

1, 71

Factors of 77

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

1, 7, 11, 77

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71 and 77, than apply into the LCM equation.

GCF(71,77) = 1
LCM(71,77) = ( 71 × 77) / 1
LCM(71,77) = 5467 / 1
LCM(71,77) = 5467

(i) The LCM of 77 and 71 is associative

LCM of 71 and 77 = LCM of 77 and 71

1. What is the LCM of 71 and 77?

Answer: LCM of 71 and 77 is 5467.

2. What are the Factors of 71?

Answer: Factors of 71 are 1, 71. There are 2 integers that are factors of 71. The greatest factor of 71 is 71.

3. 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.

4. How to Find the LCM of 71 and 77?

Answer:

Least Common Multiple of 71 and 77 = 5467

Step 1: Find the prime factorization of 71

71 = 71

Step 2: Find the prime factorization of 77

77 = 7 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 = 5467 = 7 x 11 x 71

Step 4: Therefore, the least common multiple of 71 and 77 is 5467.