Least Common Multiple (LCM) of 32 and 121
The least common multiple (LCM) of 32 and 121 is 3872.
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 32 and 121?
First, calculate the GCD of 32 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 121 = 0 remainder 32 |
| 2 | 121 ÷ 32 = 3 remainder 25 |
| 3 | 32 ÷ 25 = 1 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 71 | 2769 |
| 103 and 11 | 1133 |
| 160 and 183 | 29280 |
| 112 and 140 | 560 |
| 46 and 78 | 1794 |