Least Common Multiple (LCM) of 100 and 142
The least common multiple (LCM) of 100 and 142 is 7100.
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 100 and 142?
First, calculate the GCD of 100 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 142 = 0 remainder 100 |
| 2 | 142 ÷ 100 = 1 remainder 42 |
| 3 | 100 ÷ 42 = 2 remainder 16 |
| 4 | 42 ÷ 16 = 2 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 29 | 783 |
| 58 and 58 | 58 |
| 36 and 50 | 900 |
| 21 and 77 | 231 |
| 80 and 20 | 80 |