Least Common Multiple (LCM) of 68 and 100
The least common multiple (LCM) of 68 and 100 is 1700.
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 100?
First, calculate the GCD of 68 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 100 = 0 remainder 68 |
| 2 | 100 ÷ 68 = 1 remainder 32 |
| 3 | 68 ÷ 32 = 2 remainder 4 |
| 4 | 32 ÷ 4 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 34 | 5406 |
| 100 and 69 | 6900 |
| 58 and 122 | 3538 |
| 10 and 142 | 710 |
| 109 and 97 | 10573 |