Least Common Multiple of 83 and 84
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 83 and 84 the smallest integer that is 6972 that is divisible by both numbers.
Least Common Multiple (LCM) of 83 and 84 is 6972.
LCM(83,84) = 6972
LCM of 83 and 84
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 83 and 84 by Prime method
- Least Common Multiple of 83 and 84 with GCF Formula
LCM of 83 and 84 is 6972
Least common multiple can be found by multiplying the highest exponent prime factors of 83 and 84. First we will calculate the prime factors of 83 and 84.
Prime Factorization of 83
| 83 | 83 |
| 1 |
Prime factors of 83 are 83. Prime factorization of 83 in exponential form is:
83 = 831
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
Now multiplying the highest exponent prime factors to calculate the LCM of 83 and 84.
LCM(83,84) = 22×31×71×831
LCM(83,84) = 6972
Factors of 83
List of positive integer factors of 83 that divides 83 without a remainder.
1, 83
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
Least Common Multiple of 83 and 84 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 83 and 84, than apply into the LCM equation.
GCF(83,84) = 1
LCM(83,84) = ( 83 × 84) / 1
LCM(83,84) = 6972 / 1
LCM(83,84) = 6972
Properties of LCM 83 and 84
(i) The LCM of 84 and 83 is associative
LCM of 83 and 84 = LCM of 84 and 83
Related Least Common Multiples of 83
Related Least Common Multiples of 84
Frequently Asked Questions on LCM of 83 and 84
1. What is the LCM of 83 and 84?
Answer: LCM of 83 and 84 is 6972.
2. What are the Factors of 83?
Answer: Factors of 83 are 1, 83. There are 2 integers that are factors of 83. The greatest factor of 83 is 83.
3. 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.
4. How to Find the LCM of 83 and 84?
Answer:
Least Common Multiple of 83 and 84 = 6972
Step 1: Find the prime factorization of 83
83 = 83
Step 2: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6972 = 2 x 2 x 3 x 7 x 83
Step 4: Therefore, the least common multiple of 83 and 84 is 6972.