Least Common Multiple of 61 and 67

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

• Least Common Multiple of 61 and 67 by Prime method
• Least Common Multiple of 61 and 67 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 61 and 67. First we will calculate the prime factors of 61 and 67.

Prime Factorization of 61

Prime factors of 61 are 61. Prime factorization of 61 in exponential form is:

61 = 61¹

Prime Factorization of 67

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

67 = 67¹

Now multiplying the highest exponent prime factors to calculate the LCM of 61 and 67.

LCM(61,67) = 61¹×67¹
LCM(61,67) = 4087

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1, 61

Factors of 67

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

1, 67

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61 and 67, than apply into the LCM equation.

GCF(61,67) = 1
LCM(61,67) = ( 61 × 67) / 1
LCM(61,67) = 4087 / 1
LCM(61,67) = 4087

(i) The LCM of 67 and 61 is associative

LCM of 61 and 67 = LCM of 67 and 61

1. What is the LCM of 61 and 67?

Answer: LCM of 61 and 67 is 4087.

2. What are the Factors of 61?

Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.

3. 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.

4. How to Find the LCM of 61 and 67?

Answer:

Least Common Multiple of 61 and 67 = 4087

Step 1: Find the prime factorization of 61

61 = 61

Step 2: Find the prime factorization of 67

67 = 67

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

LCM = 4087 = 61 x 67

Step 4: Therefore, the least common multiple of 61 and 67 is 4087.