Least Common Multiple of 67 and 30
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 30 the smallest integer that is 2010 that is divisible by both numbers.
Least Common Multiple (LCM) of 67 and 30 is 2010.
LCM(67,30) = 2010
LCM of 67 and 30
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 67 and 30 by Prime method
- Least Common Multiple of 67 and 30 with GCF Formula
LCM of 67 and 30 is 2010
Least common multiple can be found by multiplying the highest exponent prime factors of 67 and 30. First we will calculate the prime factors of 67 and 30.
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 30
| 2 | 30 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:
30 = 21×31×51
Now multiplying the highest exponent prime factors to calculate the LCM of 67 and 30.
LCM(67,30) = 21×31×51×671
LCM(67,30) = 2010
Factors of 67
List of positive integer factors of 67 that divides 67 without a remainder.
1, 67
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1, 2, 3, 5, 6, 10, 15, 30
Least Common Multiple of 67 and 30 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 30, than apply into the LCM equation.
GCF(67,30) = 1
LCM(67,30) = ( 67 × 30) / 1
LCM(67,30) = 2010 / 1
LCM(67,30) = 2010
Properties of LCM 67 and 30
(i) The LCM of 30 and 67 is associative
LCM of 67 and 30 = LCM of 30 and 67
Related Least Common Multiples of 67
Related Least Common Multiples of 30
Frequently Asked Questions on LCM of 67 and 30
1. What is the LCM of 67 and 30?
Answer: LCM of 67 and 30 is 2010.
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 30?
Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.
4. How to Find the LCM of 67 and 30?
Answer:
Least Common Multiple of 67 and 30 = 2010
Step 1: Find the prime factorization of 67
67 = 67
Step 2: Find the prime factorization of 30
30 = 2 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2010 = 2 x 3 x 5 x 67
Step 4: Therefore, the least common multiple of 67 and 30 is 2010.
