Least Common Multiple of 71 and 74

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

• Least Common Multiple of 71 and 74 by Prime method
• Least Common Multiple of 71 and 74 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 71 and 74. First we will calculate the prime factors of 71 and 74.

Prime Factorization of 71

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

71 = 71¹

Prime Factorization of 74

Prime factors of 74 are 2,37. Prime factorization of 74 in exponential form is:

74 = 2¹×37¹

Now multiplying the highest exponent prime factors to calculate the LCM of 71 and 74.

LCM(71,74) = 2¹×37¹×71¹
LCM(71,74) = 5254

Factors of 71

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

1, 71

Factors of 74

List of positive integer factors of 74 that divides 74 without a remainder.

1, 2, 37, 74

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71 and 74, than apply into the LCM equation.

GCF(71,74) = 1
LCM(71,74) = ( 71 × 74) / 1
LCM(71,74) = 5254 / 1
LCM(71,74) = 5254

(i) The LCM of 74 and 71 is associative

LCM of 71 and 74 = LCM of 74 and 71

1. What is the LCM of 71 and 74?

Answer: LCM of 71 and 74 is 5254.

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 74?

Answer: Factors of 74 are 1, 2, 37, 74. There are 4 integers that are factors of 74. The greatest factor of 74 is 74.

4. How to Find the LCM of 71 and 74?

Answer:

Least Common Multiple of 71 and 74 = 5254

Step 1: Find the prime factorization of 71

71 = 71

Step 2: Find the prime factorization of 74

74 = 2 x 37

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

LCM = 5254 = 2 x 37 x 71

Step 4: Therefore, the least common multiple of 71 and 74 is 5254.