Least Common Multiple (LCM) of 87 and 154
The least common multiple (LCM) of 87 and 154 is 13398.
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 154?
First, calculate the GCD of 87 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 154 = 0 remainder 87 |
| 2 | 154 ÷ 87 = 1 remainder 67 |
| 3 | 87 ÷ 67 = 1 remainder 20 |
| 4 | 67 ÷ 20 = 3 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 70 | 1120 |
| 86 and 157 | 13502 |
| 198 and 92 | 9108 |
| 156 and 55 | 8580 |
| 36 and 47 | 1692 |