Least Common Multiple (LCM) of 121 and 75
The least common multiple (LCM) of 121 and 75 is 9075.
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 75?
First, calculate the GCD of 121 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 75 = 1 remainder 46 |
| 2 | 75 ÷ 46 = 1 remainder 29 |
| 3 | 46 ÷ 29 = 1 remainder 17 |
| 4 | 29 ÷ 17 = 1 remainder 12 |
| 5 | 17 ÷ 12 = 1 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 79 | 15484 |
| 127 and 160 | 20320 |
| 155 and 72 | 11160 |
| 173 and 38 | 6574 |
| 84 and 153 | 4284 |