Least Common Multiple (LCM) of 32 and 140
The least common multiple (LCM) of 32 and 140 is 1120.
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 140?
First, calculate the GCD of 32 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 140 = 0 remainder 32 |
| 2 | 140 ÷ 32 = 4 remainder 12 |
| 3 | 32 ÷ 12 = 2 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 135 | 2565 |
| 110 and 146 | 8030 |
| 186 and 170 | 15810 |
| 126 and 99 | 1386 |
| 167 and 75 | 12525 |