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 |
|---|---|
| 44 and 71 | 3124 |
| 158 and 129 | 20382 |
| 51 and 99 | 1683 |
| 36 and 23 | 828 |
| 153 and 191 | 29223 |