Least Common Multiple (LCM) of 140 and 87
The least common multiple (LCM) of 140 and 87 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 140 and 87?
First, calculate the GCD of 140 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 87 = 1 remainder 53 |
| 2 | 87 ÷ 53 = 1 remainder 34 |
| 3 | 53 ÷ 34 = 1 remainder 19 |
| 4 | 34 ÷ 19 = 1 remainder 15 |
| 5 | 19 ÷ 15 = 1 remainder 4 |
| 6 | 15 ÷ 4 = 3 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 125 | 2375 |
| 150 and 93 | 4650 |
| 152 and 143 | 21736 |
| 68 and 87 | 5916 |
| 121 and 178 | 21538 |