Least Common Multiple (LCM) of 120 and 99
The least common multiple (LCM) of 120 and 99 is 3960.
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 120 and 99?
First, calculate the GCD of 120 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 99 = 1 remainder 21 |
| 2 | 99 ÷ 21 = 4 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 130 | 25090 |
| 13 and 18 | 234 |
| 124 and 125 | 15500 |
| 36 and 121 | 4356 |
| 173 and 48 | 8304 |