Least Common Multiple (LCM) of 90 and 142
The least common multiple (LCM) of 90 and 142 is 6390.
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 90 and 142?
First, calculate the GCD of 90 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 142 = 0 remainder 90 |
| 2 | 142 ÷ 90 = 1 remainder 52 |
| 3 | 90 ÷ 52 = 1 remainder 38 |
| 4 | 52 ÷ 38 = 1 remainder 14 |
| 5 | 38 ÷ 14 = 2 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 55 | 2695 |
| 138 and 75 | 3450 |
| 31 and 195 | 6045 |
| 67 and 111 | 7437 |
| 21 and 104 | 2184 |