Least Common Multiple of 67 and 3

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

• Least Common Multiple of 67 and 3 by Prime method
• Least Common Multiple of 67 and 3 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67 and 3. First we will calculate the prime factors of 67 and 3.

Prime Factorization of 67

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

67 = 67¹

Prime Factorization of 3

Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:

3 = 3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67 and 3.

LCM(67,3) = 3¹×67¹
LCM(67,3) = 201

Factors of 67

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

1, 67

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67 and 3, than apply into the LCM equation.

GCF(67,3) = 1
LCM(67,3) = ( 67 × 3) / 1
LCM(67,3) = 201 / 1
LCM(67,3) = 201

(i) The LCM of 3 and 67 is associative

LCM of 67 and 3 = LCM of 3 and 67

1. What is the LCM of 67 and 3?

Answer: LCM of 67 and 3 is 201.

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 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

4. How to Find the LCM of 67 and 3?

Answer:

Least Common Multiple of 67 and 3 = 201

Step 1: Find the prime factorization of 67

67 = 67

Step 2: Find the prime factorization of 3

3 = 3

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

LCM = 201 = 3 x 67

Step 4: Therefore, the least common multiple of 67 and 3 is 201.