Least Common Multiple (LCM) of 87 and 140
The least common multiple (LCM) of 87 and 140 is 12180.
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 140?
First, calculate the GCD of 87 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 140 = 0 remainder 87 |
| 2 | 140 ÷ 87 = 1 remainder 53 |
| 3 | 87 ÷ 53 = 1 remainder 34 |
| 4 | 53 ÷ 34 = 1 remainder 19 |
| 5 | 34 ÷ 19 = 1 remainder 15 |
| 6 | 19 ÷ 15 = 1 remainder 4 |
| 7 | 15 ÷ 4 = 3 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 113 | 20792 |
| 175 and 83 | 14525 |
| 119 and 88 | 10472 |
| 159 and 56 | 8904 |
| 164 and 11 | 1804 |