Least Common Multiple (LCM) of 87 and 20
The least common multiple (LCM) of 87 and 20 is 1740.
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 20?
First, calculate the GCD of 87 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 20 = 4 remainder 7 |
| 2 | 20 ÷ 7 = 2 remainder 6 |
| 3 | 7 ÷ 6 = 1 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 112 | 3024 |
| 48 and 140 | 1680 |
| 150 and 10 | 150 |
| 193 and 183 | 35319 |
| 180 and 68 | 3060 |