Least Common Multiple (LCM) of 151 and 105
The least common multiple (LCM) of 151 and 105 is 15855.
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 151 and 105?
First, calculate the GCD of 151 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 151 ÷ 105 = 1 remainder 46 |
| 2 | 105 ÷ 46 = 2 remainder 13 |
| 3 | 46 ÷ 13 = 3 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 193 | 32424 |
| 65 and 66 | 4290 |
| 80 and 69 | 5520 |
| 132 and 56 | 1848 |
| 153 and 89 | 13617 |