Least Common Multiple (LCM) of 90 and 137
The least common multiple (LCM) of 90 and 137 is 12330.
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 90 and 137?
First, calculate the GCD of 90 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 137 = 0 remainder 90 |
| 2 | 137 ÷ 90 = 1 remainder 47 |
| 3 | 90 ÷ 47 = 1 remainder 43 |
| 4 | 47 ÷ 43 = 1 remainder 4 |
| 5 | 43 ÷ 4 = 10 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 123 | 5289 |
| 128 and 145 | 18560 |
| 161 and 101 | 16261 |
| 144 and 162 | 1296 |
| 60 and 137 | 8220 |