Least Common Multiple of 67 and 71

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

• Least Common Multiple of 67 and 71 by Prime method
• Least Common Multiple of 67 and 71 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67 and 71. First we will calculate the prime factors of 67 and 71.

Prime Factorization of 67

Prime factors of 67 are 67. Prime factorization of 67 in exponential form is:

67 = 67¹

Prime Factorization of 71

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

71 = 71¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67 and 71.

LCM(67,71) = 67¹×71¹
LCM(67,71) = 4757

Factors of 67

List of positive integer factors of 67 that divides 67 without a remainder.

1, 67

Factors of 71

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

1, 71

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67 and 71, than apply into the LCM equation.

GCF(67,71) = 1
LCM(67,71) = ( 67 × 71) / 1
LCM(67,71) = 4757 / 1
LCM(67,71) = 4757

(i) The LCM of 71 and 67 is associative

LCM of 67 and 71 = LCM of 71 and 67

1. What is the LCM of 67 and 71?

Answer: LCM of 67 and 71 is 4757.

2. What are the Factors of 67?

Answer: Factors of 67 are 1, 67. There are 2 integers that are factors of 67. The greatest factor of 67 is 67.

3. 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.

4. How to Find the LCM of 67 and 71?

Answer:

Least Common Multiple of 67 and 71 = 4757

Step 1: Find the prime factorization of 67

67 = 67

Step 2: Find the prime factorization of 71

71 = 71

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

LCM = 4757 = 67 x 71

Step 4: Therefore, the least common multiple of 67 and 71 is 4757.