Least Common Multiple (LCM) of 142 and 87
The least common multiple (LCM) of 142 and 87 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 142 and 87?
First, calculate the GCD of 142 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 87 = 1 remainder 55 |
| 2 | 87 ÷ 55 = 1 remainder 32 |
| 3 | 55 ÷ 32 = 1 remainder 23 |
| 4 | 32 ÷ 23 = 1 remainder 9 |
| 5 | 23 ÷ 9 = 2 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 99 | 10197 |
| 80 and 143 | 11440 |
| 108 and 17 | 1836 |
| 155 and 200 | 6200 |
| 131 and 115 | 15065 |