Least Common Multiple of 67 and 68

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 67 and 68 the smallest integer that is 4556 that is divisible by both numbers.

Least Common Multiple (LCM) of 67 and 68 is 4556.

LCM(67,68) = 4556

LCM of 67 and 68

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

LCM of:
and

Least Common Multiple of 67 and 68

LCM of 67 and 68 is 4556

Least common multiple can be found by multiplying the highest exponent prime factors of 67 and 68. First we will calculate the prime factors of 67 and 68.

Prime Factorization of 67


67 67
1

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

67 = 671

Prime Factorization of 68


2 68
2 34
17 17
1

Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:

68 = 22×171

Now multiplying the highest exponent prime factors to calculate the LCM of 67 and 68.

LCM(67,68) = 22×171×671
LCM(67,68) = 4556

Factors of 67

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

1, 67

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1, 2, 4, 17, 34, 68

Least Common Multiple of 67 and 68 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67 and 68, than apply into the LCM equation.

GCF(67,68) = 1
LCM(67,68) = ( 67 × 68) / 1
LCM(67,68) = 4556 / 1
LCM(67,68) = 4556

Properties of LCM 67 and 68

(i) The LCM of 68 and 67 is associative

LCM of 67 and 68 = LCM of 68 and 67

Related Least Common Multiples of 67

Related Least Common Multiples of 68

Frequently Asked Questions on LCM of 67 and 68

1. What is the LCM of 67 and 68?

Answer: LCM of 67 and 68 is 4556.

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 68?

Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.

4. How to Find the LCM of 67 and 68?

Answer:

Least Common Multiple of 67 and 68 = 4556

Step 1: Find the prime factorization of 67

67 = 67

Step 2: Find the prime factorization of 68

68 = 2 x 2 x 17

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

LCM = 4556 = 2 x 2 x 17 x 67

Step 4: Therefore, the least common multiple of 67 and 68 is 4556.