Least Common Multiple (LCM) of 87 and 164
The least common multiple (LCM) of 87 and 164 is 14268.
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 164?
First, calculate the GCD of 87 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 164 = 0 remainder 87 |
| 2 | 164 ÷ 87 = 1 remainder 77 |
| 3 | 87 ÷ 77 = 1 remainder 10 |
| 4 | 77 ÷ 10 = 7 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 110 | 21010 |
| 115 and 49 | 5635 |
| 103 and 155 | 15965 |
| 169 and 39 | 507 |
| 138 and 135 | 6210 |