Least Common Multiple (LCM) of 117 and 90
The least common multiple (LCM) of 117 and 90 is 1170.
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 117 and 90?
First, calculate the GCD of 117 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 90 = 1 remainder 27 |
| 2 | 90 ÷ 27 = 3 remainder 9 |
| 3 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 129 | 129 |
| 180 and 191 | 34380 |
| 126 and 51 | 2142 |
| 137 and 21 | 2877 |
| 170 and 48 | 4080 |