Least Common Multiple (LCM) of 34 and 151
The least common multiple (LCM) of 34 and 151 is 5134.
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 151?
First, calculate the GCD of 34 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 151 = 0 remainder 34 |
| 2 | 151 ÷ 34 = 4 remainder 15 |
| 3 | 34 ÷ 15 = 2 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 145 | 3915 |
| 45 and 128 | 5760 |
| 184 and 188 | 8648 |
| 147 and 50 | 7350 |
| 119 and 104 | 12376 |