Least Common Multiple (LCM) of 90 and 125
The least common multiple (LCM) of 90 and 125 is 2250.
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 125?
First, calculate the GCD of 90 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 125 = 0 remainder 90 |
| 2 | 125 ÷ 90 = 1 remainder 35 |
| 3 | 90 ÷ 35 = 2 remainder 20 |
| 4 | 35 ÷ 20 = 1 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 118 | 6018 |
| 146 and 188 | 13724 |
| 46 and 145 | 6670 |
| 85 and 178 | 15130 |
| 30 and 53 | 1590 |