Least Common Multiple (LCM) of 90 and 103
The least common multiple (LCM) of 90 and 103 is 9270.
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 103?
First, calculate the GCD of 90 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 103 = 0 remainder 90 |
| 2 | 103 ÷ 90 = 1 remainder 13 |
| 3 | 90 ÷ 13 = 6 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 104 | 9672 |
| 170 and 166 | 14110 |
| 156 and 182 | 1092 |
| 154 and 18 | 1386 |
| 180 and 97 | 17460 |