Least Common Multiple (LCM) of 101 and 140
The least common multiple (LCM) of 101 and 140 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 101 and 140?
First, calculate the GCD of 101 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 140 = 0 remainder 101 |
| 2 | 140 ÷ 101 = 1 remainder 39 |
| 3 | 101 ÷ 39 = 2 remainder 23 |
| 4 | 39 ÷ 23 = 1 remainder 16 |
| 5 | 23 ÷ 16 = 1 remainder 7 |
| 6 | 16 ÷ 7 = 2 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 47 | 6345 |
| 39 and 17 | 663 |
| 15 and 25 | 75 |
| 145 and 178 | 25810 |
| 117 and 138 | 5382 |