Least Common Multiple (LCM) of 87 and 121
The least common multiple (LCM) of 87 and 121 is 10527.
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 121?
First, calculate the GCD of 87 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 121 = 0 remainder 87 |
| 2 | 121 ÷ 87 = 1 remainder 34 |
| 3 | 87 ÷ 34 = 2 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 |
|---|---|
| 112 and 39 | 4368 |
| 39 and 31 | 1209 |
| 194 and 45 | 8730 |
| 144 and 160 | 1440 |
| 89 and 21 | 1869 |