Least Common Multiple (LCM) of 34 and 149
The least common multiple (LCM) of 34 and 149 is 5066.
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 149?
First, calculate the GCD of 34 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 149 = 0 remainder 34 |
| 2 | 149 ÷ 34 = 4 remainder 13 |
| 3 | 34 ÷ 13 = 2 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 136 | 8568 |
| 95 and 177 | 16815 |
| 114 and 183 | 6954 |
| 38 and 59 | 2242 |
| 188 and 112 | 5264 |