Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 86 and 104 the smallest integer that is 4472 that is divisible by both numbers.
Least Common Multiple (LCM) of 86 and 104 is 4472.
LCM(86,104) = 4472
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 86 and 104. First we will calculate the prime factors of 86 and 104.
Prime Factorization of 86
2 | 86 |
43 | 43 |
1 |
Prime factors of 86 are 2,43. Prime factorization of 86 in exponential form is:
86 = 21×431
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 86 and 104.
LCM(86,104) = 23×131×431
LCM(86,104) = 4472
Factors of 86
List of positive integer factors of 86 that divides 86 without a remainder.
1, 2, 43, 86
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 86 and 104, than apply into the LCM equation.
GCF(86,104) = 2
LCM(86,104) = ( 86 × 104) / 2
LCM(86,104) = 8944 / 2
LCM(86,104) = 4472
(i) The LCM of 104 and 86 is associative
LCM of 86 and 104 = LCM of 104 and 86
1. What is the LCM of 86 and 104?
Answer: LCM of 86 and 104 is 4472.
2. What are the Factors of 86?
Answer: Factors of 86 are 1, 2, 43, 86. There are 4 integers that are factors of 86. The greatest factor of 86 is 86.
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 86 and 104?
Answer:
Least Common Multiple of 86 and 104 = 4472
Step 1: Find the prime factorization of 86
86 = 2 x 43
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 = 4472 = 2 x 2 x 2 x 13 x 43
Step 4: Therefore, the least common multiple of 86 and 104 is 4472.