Least Common Multiple (LCM) of 87 and 106
The least common multiple (LCM) of 87 and 106 is 9222.
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 106?
First, calculate the GCD of 87 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 106 = 0 remainder 87 |
| 2 | 106 ÷ 87 = 1 remainder 19 |
| 3 | 87 ÷ 19 = 4 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 192 | 4800 |
| 165 and 111 | 6105 |
| 182 and 80 | 7280 |
| 140 and 44 | 1540 |
| 54 and 162 | 162 |