Least Common Multiple of 84 and 103
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 84 and 103 the smallest integer that is 8652 that is divisible by both numbers.
Least Common Multiple (LCM) of 84 and 103 is 8652.
LCM(84,103) = 8652
LCM of 84 and 103
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 84 and 103 by Prime method
- Least Common Multiple of 84 and 103 with GCF Formula
LCM of 84 and 103 is 8652
Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 103. First we will calculate the prime factors of 84 and 103.
Prime Factorization of 84
| 2 | 84 |
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:
84 = 22×31×71
Prime Factorization of 103
| 103 | 103 |
| 1 |
Prime factors of 103 are 103. Prime factorization of 103 in exponential form is:
103 = 1031
Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 103.
LCM(84,103) = 22×31×71×1031
LCM(84,103) = 8652
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 103
List of positive integer factors of 103 that divides 103 without a remainder.
1, 103
Least Common Multiple of 84 and 103 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 103, than apply into the LCM equation.
GCF(84,103) = 1
LCM(84,103) = ( 84 × 103) / 1
LCM(84,103) = 8652 / 1
LCM(84,103) = 8652
Properties of LCM 84 and 103
(i) The LCM of 103 and 84 is associative
LCM of 84 and 103 = LCM of 103 and 84
Related Least Common Multiples of 84
Related Least Common Multiples of 103
Frequently Asked Questions on LCM of 84 and 103
1. What is the LCM of 84 and 103?
Answer: LCM of 84 and 103 is 8652.
2. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
3. What are the Factors of 103?
Answer: Factors of 103 are 1, 103. There are 2 integers that are factors of 103. The greatest factor of 103 is 103.
4. How to Find the LCM of 84 and 103?
Answer:
Least Common Multiple of 84 and 103 = 8652
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 103
103 = 103
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8652 = 2 x 2 x 3 x 7 x 103
Step 4: Therefore, the least common multiple of 84 and 103 is 8652.
