Least Common Multiple (LCM) of 101 and 142
The least common multiple (LCM) of 101 and 142 is 14342.
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 142?
First, calculate the GCD of 101 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 142 = 0 remainder 101 |
| 2 | 142 ÷ 101 = 1 remainder 41 |
| 3 | 101 ÷ 41 = 2 remainder 19 |
| 4 | 41 ÷ 19 = 2 remainder 3 |
| 5 | 19 ÷ 3 = 6 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 185 | 5180 |
| 13 and 172 | 2236 |
| 93 and 157 | 14601 |
| 163 and 19 | 3097 |
| 96 and 80 | 480 |