Least Common Multiple (LCM) of 121 and 144
The least common multiple (LCM) of 121 and 144 is 17424.
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 121 and 144?
First, calculate the GCD of 121 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 144 = 0 remainder 121 |
| 2 | 144 ÷ 121 = 1 remainder 23 |
| 3 | 121 ÷ 23 = 5 remainder 6 |
| 4 | 23 ÷ 6 = 3 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 99 | 4257 |
| 126 and 121 | 15246 |
| 69 and 150 | 3450 |
| 31 and 59 | 1829 |
| 81 and 15 | 405 |