Least Common Multiple of 67 and 74

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

• Least Common Multiple of 67 and 74 by Prime method
• Least Common Multiple of 67 and 74 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67 and 74. First we will calculate the prime factors of 67 and 74.

Prime Factorization of 67

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

67 = 67¹

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 67 and 74.

LCM(67,74) = 2¹×37¹×67¹
LCM(67,74) = 4958

Factors of 67

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

1, 67

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 67 and 74, than apply into the LCM equation.

GCF(67,74) = 1
LCM(67,74) = ( 67 × 74) / 1
LCM(67,74) = 4958 / 1
LCM(67,74) = 4958

(i) The LCM of 74 and 67 is associative

LCM of 67 and 74 = LCM of 74 and 67

1. What is the LCM of 67 and 74?

Answer: LCM of 67 and 74 is 4958.

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 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 67 and 74?

Answer:

Least Common Multiple of 67 and 74 = 4958

Step 1: Find the prime factorization of 67

67 = 67

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 = 4958 = 2 x 37 x 67

Step 4: Therefore, the least common multiple of 67 and 74 is 4958.