Least Common Multiple (LCM) of 121 and 175
The least common multiple (LCM) of 121 and 175 is 21175.
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 175?
First, calculate the GCD of 121 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 175 = 0 remainder 121 |
| 2 | 175 ÷ 121 = 1 remainder 54 |
| 3 | 121 ÷ 54 = 2 remainder 13 |
| 4 | 54 ÷ 13 = 4 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 10 | 210 |
| 146 and 180 | 13140 |
| 185 and 128 | 23680 |
| 85 and 16 | 1360 |
| 132 and 166 | 10956 |