Least Common Multiple (LCM) of 34 and 99
The least common multiple (LCM) of 34 and 99 is 3366.
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 99?
First, calculate the GCD of 34 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 99 = 0 remainder 34 |
| 2 | 99 ÷ 34 = 2 remainder 31 |
| 3 | 34 ÷ 31 = 1 remainder 3 |
| 4 | 31 ÷ 3 = 10 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 115 | 17020 |
| 60 and 157 | 9420 |
| 189 and 59 | 11151 |
| 15 and 47 | 705 |
| 10 and 182 | 910 |