Least Common Multiple (LCM) of 90 and 68
The least common multiple (LCM) of 90 and 68 is 3060.
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 68?
First, calculate the GCD of 90 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 68 = 1 remainder 22 |
| 2 | 68 ÷ 22 = 3 remainder 2 |
| 3 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 138 | 21390 |
| 121 and 172 | 20812 |
| 119 and 106 | 12614 |
| 152 and 108 | 4104 |
| 30 and 15 | 30 |