Least Common Multiple (LCM) of 68 and 90
The least common multiple (LCM) of 68 and 90 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 68 and 90?
First, calculate the GCD of 68 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 90 = 0 remainder 68 |
| 2 | 90 ÷ 68 = 1 remainder 22 |
| 3 | 68 ÷ 22 = 3 remainder 2 |
| 4 | 22 ÷ 2 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 75 | 7800 |
| 62 and 36 | 1116 |
| 36 and 140 | 1260 |
| 124 and 23 | 2852 |
| 97 and 53 | 5141 |