Least Common Multiple (LCM) of 101 and 120
The least common multiple (LCM) of 101 and 120 is 12120.
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 101 and 120?
First, calculate the GCD of 101 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 120 = 0 remainder 101 |
| 2 | 120 ÷ 101 = 1 remainder 19 |
| 3 | 101 ÷ 19 = 5 remainder 6 |
| 4 | 19 ÷ 6 = 3 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 82 | 6314 |
| 174 and 147 | 8526 |
| 199 and 73 | 14527 |
| 132 and 174 | 3828 |
| 27 and 196 | 5292 |