Least Common Multiple (LCM) of 68 and 120
The least common multiple (LCM) of 68 and 120 is 2040.
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 120?
First, calculate the GCD of 68 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 120 = 0 remainder 68 |
| 2 | 120 ÷ 68 = 1 remainder 52 |
| 3 | 68 ÷ 52 = 1 remainder 16 |
| 4 | 52 ÷ 16 = 3 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 90 | 6120 |
| 92 and 171 | 15732 |
| 108 and 171 | 2052 |
| 78 and 103 | 8034 |
| 127 and 130 | 16510 |