Least Common Multiple (LCM) of 100 and 68
The least common multiple (LCM) of 100 and 68 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 100 and 68?
First, calculate the GCD of 100 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 68 = 1 remainder 32 |
| 2 | 68 ÷ 32 = 2 remainder 4 |
| 3 | 32 ÷ 4 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 172 | 172 |
| 78 and 134 | 5226 |
| 176 and 172 | 7568 |
| 161 and 15 | 2415 |
| 119 and 63 | 1071 |