Least Common Multiple (LCM) of 87 and 160
The least common multiple (LCM) of 87 and 160 is 13920.
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 160?
First, calculate the GCD of 87 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 160 = 0 remainder 87 |
| 2 | 160 ÷ 87 = 1 remainder 73 |
| 3 | 87 ÷ 73 = 1 remainder 14 |
| 4 | 73 ÷ 14 = 5 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 49 | 5537 |
| 67 and 74 | 4958 |
| 19 and 64 | 1216 |
| 186 and 199 | 37014 |
| 176 and 39 | 6864 |