Least Common Multiple (LCM) of 34 and 153
The least common multiple (LCM) of 34 and 153 is 306.
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 153?
First, calculate the GCD of 34 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 153 = 0 remainder 34 |
| 2 | 153 ÷ 34 = 4 remainder 17 |
| 3 | 34 ÷ 17 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 118 | 7434 |
| 192 and 114 | 3648 |
| 113 and 146 | 16498 |
| 83 and 83 | 83 |
| 100 and 165 | 3300 |