Least Common Multiple (LCM) of 75 and 121
The least common multiple (LCM) of 75 and 121 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 75 and 121?
First, calculate the GCD of 75 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 121 = 0 remainder 75 |
| 2 | 121 ÷ 75 = 1 remainder 46 |
| 3 | 75 ÷ 46 = 1 remainder 29 |
| 4 | 46 ÷ 29 = 1 remainder 17 |
| 5 | 29 ÷ 17 = 1 remainder 12 |
| 6 | 17 ÷ 12 = 1 remainder 5 |
| 7 | 12 ÷ 5 = 2 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 196 | 7252 |
| 41 and 96 | 3936 |
| 20 and 28 | 140 |
| 116 and 145 | 580 |
| 89 and 58 | 5162 |