Least Common Multiple (LCM) of 90 and 168
The least common multiple (LCM) of 90 and 168 is 2520.
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 168?
First, calculate the GCD of 90 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 168 = 0 remainder 90 |
| 2 | 168 ÷ 90 = 1 remainder 78 |
| 3 | 90 ÷ 78 = 1 remainder 12 |
| 4 | 78 ÷ 12 = 6 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 19 | 589 |
| 34 and 84 | 1428 |
| 150 and 134 | 10050 |
| 14 and 110 | 770 |
| 105 and 111 | 3885 |