Least Common Multiple (LCM) of 90 and 34
The least common multiple (LCM) of 90 and 34 is 1530.
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 34?
First, calculate the GCD of 90 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 34 = 2 remainder 22 |
| 2 | 34 ÷ 22 = 1 remainder 12 |
| 3 | 22 ÷ 12 = 1 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 119 | 6783 |
| 158 and 63 | 9954 |
| 39 and 143 | 429 |
| 30 and 179 | 5370 |
| 168 and 98 | 1176 |