Least Common Multiple (LCM) of 87 and 155
The least common multiple (LCM) of 87 and 155 is 13485.
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 155?
First, calculate the GCD of 87 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 155 = 0 remainder 87 |
| 2 | 155 ÷ 87 = 1 remainder 68 |
| 3 | 87 ÷ 68 = 1 remainder 19 |
| 4 | 68 ÷ 19 = 3 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 37 | 555 |
| 33 and 91 | 3003 |
| 139 and 107 | 14873 |
| 70 and 84 | 420 |
| 155 and 163 | 25265 |