Least Common Multiple of 18 and 67
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 18 and 67 the smallest integer that is 1206 that is divisible by both numbers.
Least Common Multiple (LCM) of 18 and 67 is 1206.
LCM(18,67) = 1206
LCM of 18 and 67
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 18 and 67 by Prime method
- Least Common Multiple of 18 and 67 with GCF Formula
LCM of 18 and 67 is 1206
Least common multiple can be found by multiplying the highest exponent prime factors of 18 and 67. First we will calculate the prime factors of 18 and 67.
Prime Factorization of 18
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:
18 = 21×32
Prime Factorization of 67
| 67 | 67 |
| 1 |
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 18 and 67.
LCM(18,67) = 21×32×671
LCM(18,67) = 1206
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1, 2, 3, 6, 9, 18
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1, 67
Least Common Multiple of 18 and 67 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18 and 67, than apply into the LCM equation.
GCF(18,67) = 1
LCM(18,67) = ( 18 × 67) / 1
LCM(18,67) = 1206 / 1
LCM(18,67) = 1206
Properties of LCM 18 and 67
(i) The LCM of 67 and 18 is associative
LCM of 18 and 67 = LCM of 67 and 18
Related Least Common Multiples of 18
Related Least Common Multiples of 67
Frequently Asked Questions on LCM of 18 and 67
1. What is the LCM of 18 and 67?
Answer: LCM of 18 and 67 is 1206.
2. What are the Factors of 18?
Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.
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 18 and 67?
Answer:
Least Common Multiple of 18 and 67 = 1206
Step 1: Find the prime factorization of 18
18 = 2 x 3 x 3
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 = 1206 = 2 x 3 x 3 x 67
Step 4: Therefore, the least common multiple of 18 and 67 is 1206.
