Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 89 and 68 the smallest integer that is 6052 that is divisible by both numbers.
Least Common Multiple (LCM) of 89 and 68 is 6052.
LCM(89,68) = 6052
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 89 and 68. First we will calculate the prime factors of 89 and 68.
Prime Factorization of 89
89 | 89 |
1 |
Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:
89 = 891
Prime Factorization of 68
2 | 68 |
2 | 34 |
17 | 17 |
1 |
Prime factors of 68 are 2,17. Prime factorization of 68 in exponential form is:
68 = 22×171
Now multiplying the highest exponent prime factors to calculate the LCM of 89 and 68.
LCM(89,68) = 22×171×891
LCM(89,68) = 6052
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1, 89
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1, 2, 4, 17, 34, 68
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89 and 68, than apply into the LCM equation.
GCF(89,68) = 1
LCM(89,68) = ( 89 × 68) / 1
LCM(89,68) = 6052 / 1
LCM(89,68) = 6052
(i) The LCM of 68 and 89 is associative
LCM of 89 and 68 = LCM of 68 and 89
1. What is the LCM of 89 and 68?
Answer: LCM of 89 and 68 is 6052.
2. What are the Factors of 89?
Answer: Factors of 89 are 1, 89. There are 2 integers that are factors of 89. The greatest factor of 89 is 89.
3. What are the Factors of 68?
Answer: Factors of 68 are 1, 2, 4, 17, 34, 68. There are 6 integers that are factors of 68. The greatest factor of 68 is 68.
4. How to Find the LCM of 89 and 68?
Answer:
Least Common Multiple of 89 and 68 = 6052
Step 1: Find the prime factorization of 89
89 = 89
Step 2: Find the prime factorization of 68
68 = 2 x 2 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6052 = 2 x 2 x 17 x 89
Step 4: Therefore, the least common multiple of 89 and 68 is 6052.