Least Common Multiple (LCM) of 90 and 120
The least common multiple (LCM) of 90 and 120 is 360.
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 90 and 120?
First, calculate the GCD of 90 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 120 = 0 remainder 90 |
| 2 | 120 ÷ 90 = 1 remainder 30 |
| 3 | 90 ÷ 30 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 43 | 1075 |
| 110 and 105 | 2310 |
| 140 and 190 | 2660 |
| 184 and 112 | 2576 |
| 105 and 140 | 420 |