Least Common Multiple (LCM) of 155 and 87
The least common multiple (LCM) of 155 and 87 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 155 and 87?
First, calculate the GCD of 155 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 87 = 1 remainder 68 |
| 2 | 87 ÷ 68 = 1 remainder 19 |
| 3 | 68 ÷ 19 = 3 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 |
|---|---|
| 31 and 22 | 682 |
| 23 and 131 | 3013 |
| 105 and 185 | 3885 |
| 110 and 32 | 1760 |
| 178 and 36 | 3204 |