Least Common Multiple (LCM) of 87 and 142
The least common multiple (LCM) of 87 and 142 is 12354.
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 87 and 142?
First, calculate the GCD of 87 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 142 = 0 remainder 87 |
| 2 | 142 ÷ 87 = 1 remainder 55 |
| 3 | 87 ÷ 55 = 1 remainder 32 |
| 4 | 55 ÷ 32 = 1 remainder 23 |
| 5 | 32 ÷ 23 = 1 remainder 9 |
| 6 | 23 ÷ 9 = 2 remainder 5 |
| 7 | 9 ÷ 5 = 1 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 37 | 5106 |
| 146 and 168 | 12264 |
| 124 and 45 | 5580 |
| 45 and 35 | 315 |
| 63 and 93 | 1953 |