Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 68 and 69 the smallest integer that is 4692 that is divisible by both numbers.
Least Common Multiple (LCM) of 68 and 69 is 4692.
LCM(68,69) = 4692
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 68 and 69. First we will calculate the prime factors of 68 and 69.
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
Prime Factorization of 69
3 | 69 |
23 | 23 |
1 |
Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:
69 = 31×231
Now multiplying the highest exponent prime factors to calculate the LCM of 68 and 69.
LCM(68,69) = 22×31×171×231
LCM(68,69) = 4692
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1, 2, 4, 17, 34, 68
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1, 3, 23, 69
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68 and 69, than apply into the LCM equation.
GCF(68,69) = 1
LCM(68,69) = ( 68 × 69) / 1
LCM(68,69) = 4692 / 1
LCM(68,69) = 4692
(i) The LCM of 69 and 68 is associative
LCM of 68 and 69 = LCM of 69 and 68
1. What is the LCM of 68 and 69?
Answer: LCM of 68 and 69 is 4692.
2. 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.
3. What are the Factors of 69?
Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.
4. How to Find the LCM of 68 and 69?
Answer:
Least Common Multiple of 68 and 69 = 4692
Step 1: Find the prime factorization of 68
68 = 2 x 2 x 17
Step 2: Find the prime factorization of 69
69 = 3 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4692 = 2 x 2 x 3 x 17 x 23
Step 4: Therefore, the least common multiple of 68 and 69 is 4692.