Least Common Multiple (LCM) of 68 and 172
The least common multiple (LCM) of 68 and 172 is 2924.
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 172?
First, calculate the GCD of 68 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 172 = 0 remainder 68 |
| 2 | 172 ÷ 68 = 2 remainder 36 |
| 3 | 68 ÷ 36 = 1 remainder 32 |
| 4 | 36 ÷ 32 = 1 remainder 4 |
| 5 | 32 ÷ 4 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 40 | 5160 |
| 120 and 25 | 600 |
| 189 and 110 | 20790 |
| 96 and 61 | 5856 |
| 125 and 175 | 875 |