Least Common Multiple (LCM) of 20 and 87
The least common multiple (LCM) of 20 and 87 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 20 and 87?
First, calculate the GCD of 20 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 87 = 0 remainder 20 |
| 2 | 87 ÷ 20 = 4 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 129 | 7095 |
| 180 and 18 | 180 |
| 163 and 113 | 18419 |
| 109 and 128 | 13952 |
| 167 and 23 | 3841 |