Least Common Multiple (LCM) of 87 and 159
The least common multiple (LCM) of 87 and 159 is 4611.
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 159?
First, calculate the GCD of 87 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 159 = 0 remainder 87 |
| 2 | 159 ÷ 87 = 1 remainder 72 |
| 3 | 87 ÷ 72 = 1 remainder 15 |
| 4 | 72 ÷ 15 = 4 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 76 | 988 |
| 45 and 170 | 1530 |
| 93 and 114 | 3534 |
| 197 and 67 | 13199 |
| 87 and 167 | 14529 |