Least Common Multiple (LCM) of 87 and 170
The least common multiple (LCM) of 87 and 170 is 14790.
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 170?
First, calculate the GCD of 87 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 170 = 0 remainder 87 |
| 2 | 170 ÷ 87 = 1 remainder 83 |
| 3 | 87 ÷ 83 = 1 remainder 4 |
| 4 | 83 ÷ 4 = 20 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 44 | 572 |
| 140 and 168 | 840 |
| 150 and 80 | 1200 |
| 126 and 92 | 5796 |
| 14 and 48 | 336 |