Least Common Multiple (LCM) of 34 and 90
The least common multiple (LCM) of 34 and 90 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 34 and 90?
First, calculate the GCD of 34 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 90 = 0 remainder 34 |
| 2 | 90 ÷ 34 = 2 remainder 22 |
| 3 | 34 ÷ 22 = 1 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 27 | 3024 |
| 72 and 119 | 8568 |
| 74 and 154 | 5698 |
| 45 and 16 | 720 |
| 99 and 175 | 17325 |