Least Common Multiple (LCM) of 142 and 100
The least common multiple (LCM) of 142 and 100 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 142 and 100?
First, calculate the GCD of 142 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 100 = 1 remainder 42 |
| 2 | 100 ÷ 42 = 2 remainder 16 |
| 3 | 42 ÷ 16 = 2 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 126 | 2394 |
| 73 and 156 | 11388 |
| 96 and 182 | 8736 |
| 83 and 143 | 11869 |
| 126 and 110 | 6930 |