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 104 the smallest integer that is 2184 that is divisible by both numbers.
Least Common Multiple (LCM) of 84 and 104 is 2184.
LCM(84,104) = 2184
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 104. First we will calculate the prime factors of 84 and 104.
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 104
2 | 104 |
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 104 are 2,13. Prime factorization of 104 in exponential form is:
104 = 23×131
Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 104.
LCM(84,104) = 23×31×71×131
LCM(84,104) = 2184
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 104
List of positive integer factors of 104 that divides 104 without a remainder.
1, 2, 4, 8, 13, 26, 52, 104
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 104, than apply into the LCM equation.
GCF(84,104) = 4
LCM(84,104) = ( 84 × 104) / 4
LCM(84,104) = 8736 / 4
LCM(84,104) = 2184
(i) The LCM of 104 and 84 is associative
LCM of 84 and 104 = LCM of 104 and 84
1. What is the LCM of 84 and 104?
Answer: LCM of 84 and 104 is 2184.
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 104?
Answer: Factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104. There are 8 integers that are factors of 104. The greatest factor of 104 is 104.
4. How to Find the LCM of 84 and 104?
Answer:
Least Common Multiple of 84 and 104 = 2184
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 104
104 = 2 x 2 x 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2184 = 2 x 2 x 2 x 3 x 7 x 13
Step 4: Therefore, the least common multiple of 84 and 104 is 2184.