Least Common Multiple (LCM) of 87 and 111
The least common multiple (LCM) of 87 and 111 is 3219.
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 111?
First, calculate the GCD of 87 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 111 = 0 remainder 87 |
| 2 | 111 ÷ 87 = 1 remainder 24 |
| 3 | 87 ÷ 24 = 3 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 26 | 2080 |
| 68 and 161 | 10948 |
| 53 and 181 | 9593 |
| 100 and 110 | 1100 |
| 174 and 170 | 14790 |