Least Common Multiple of 67 and 69

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

• Least Common Multiple of 67 and 69 by Prime method
• Least Common Multiple of 67 and 69 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 67 and 69. First we will calculate the prime factors of 67 and 69.

Prime Factorization of 67

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

67 = 67¹

Prime Factorization of 69

Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:

69 = 3¹×23¹

Now multiplying the highest exponent prime factors to calculate the LCM of 67 and 69.

LCM(67,69) = 3¹×23¹×67¹
LCM(67,69) = 4623

Factors of 67

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

1, 67

Factors of 69

List of positive integer factors of 69 that divides 69 without a remainder.

1, 3, 23, 69

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67 and 69, than apply into the LCM equation.

GCF(67,69) = 1
LCM(67,69) = ( 67 × 69) / 1
LCM(67,69) = 4623 / 1
LCM(67,69) = 4623

(i) The LCM of 69 and 67 is associative

LCM of 67 and 69 = LCM of 69 and 67

1. What is the LCM of 67 and 69?

Answer: LCM of 67 and 69 is 4623.

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 69?

Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.

4. How to Find the LCM of 67 and 69?

Answer:

Least Common Multiple of 67 and 69 = 4623

Step 1: Find the prime factorization of 67

67 = 67

Step 2: Find the prime factorization of 69

69 = 3 x 23

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

LCM = 4623 = 3 x 23 x 67

Step 4: Therefore, the least common multiple of 67 and 69 is 4623.