Least Common Multiple (LCM) of 90 and 36
The least common multiple (LCM) of 90 and 36 is 180.
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 36?
First, calculate the GCD of 90 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 36 = 2 remainder 18 |
| 2 | 36 ÷ 18 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 177 | 5310 |
| 161 and 78 | 12558 |
| 32 and 196 | 1568 |
| 33 and 27 | 297 |
| 165 and 196 | 32340 |