Least Common Multiple (LCM) of 90 and 121
The least common multiple (LCM) of 90 and 121 is 10890.
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 121?
First, calculate the GCD of 90 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 121 = 0 remainder 90 |
| 2 | 121 ÷ 90 = 1 remainder 31 |
| 3 | 90 ÷ 31 = 2 remainder 28 |
| 4 | 31 ÷ 28 = 1 remainder 3 |
| 5 | 28 ÷ 3 = 9 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 48 | 2064 |
| 61 and 199 | 12139 |
| 154 and 135 | 20790 |
| 168 and 49 | 1176 |
| 176 and 126 | 11088 |