Least Common Multiple (LCM) of 68 and 37
The least common multiple (LCM) of 68 and 37 is 2516.
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 37?
First, calculate the GCD of 68 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 37 = 1 remainder 31 |
| 2 | 37 ÷ 31 = 1 remainder 6 |
| 3 | 31 ÷ 6 = 5 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 112 | 1456 |
| 173 and 187 | 32351 |
| 140 and 178 | 12460 |
| 132 and 63 | 2772 |
| 11 and 31 | 341 |