Least Common Multiple (LCM) of 90 and 200
The least common multiple (LCM) of 90 and 200 is 1800.
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 200?
First, calculate the GCD of 90 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 200 = 0 remainder 90 |
| 2 | 200 ÷ 90 = 2 remainder 20 |
| 3 | 90 ÷ 20 = 4 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 149 | 21456 |
| 157 and 61 | 9577 |
| 120 and 171 | 6840 |
| 89 and 112 | 9968 |
| 76 and 167 | 12692 |