Least Common Multiple (LCM) of 105 and 151
The least common multiple (LCM) of 105 and 151 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 105 and 151?
First, calculate the GCD of 105 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 151 = 0 remainder 105 |
| 2 | 151 ÷ 105 = 1 remainder 46 |
| 3 | 105 ÷ 46 = 2 remainder 13 |
| 4 | 46 ÷ 13 = 3 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 19 | 3268 |
| 174 and 99 | 5742 |
| 115 and 131 | 15065 |
| 72 and 79 | 5688 |
| 89 and 31 | 2759 |