Least Common Multiple (LCM) of 87 and 139
The least common multiple (LCM) of 87 and 139 is 12093.
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 139?
First, calculate the GCD of 87 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 139 = 0 remainder 87 |
| 2 | 139 ÷ 87 = 1 remainder 52 |
| 3 | 87 ÷ 52 = 1 remainder 35 |
| 4 | 52 ÷ 35 = 1 remainder 17 |
| 5 | 35 ÷ 17 = 2 remainder 1 |
| 6 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 105 | 1995 |
| 55 and 167 | 9185 |
| 25 and 16 | 400 |
| 32 and 69 | 2208 |
| 190 and 118 | 11210 |