Least Common Multiple (LCM) of 68 and 102
The least common multiple (LCM) of 68 and 102 is 204.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 68 and 102?
First, calculate the GCD of 68 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 102 = 0 remainder 68 |
| 2 | 102 ÷ 68 = 1 remainder 34 |
| 3 | 68 ÷ 34 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 74 | 3922 |
| 82 and 196 | 8036 |
| 53 and 59 | 3127 |
| 147 and 172 | 25284 |
| 47 and 61 | 2867 |