Least Common Multiple (LCM) of 140 and 101
The least common multiple (LCM) of 140 and 101 is 14140.
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 140 and 101?
First, calculate the GCD of 140 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 101 = 1 remainder 39 |
| 2 | 101 ÷ 39 = 2 remainder 23 |
| 3 | 39 ÷ 23 = 1 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 42 | 6090 |
| 125 and 158 | 19750 |
| 72 and 61 | 4392 |
| 176 and 105 | 18480 |
| 25 and 101 | 2525 |