Least Common Multiple (LCM) of 112 and 151
The least common multiple (LCM) of 112 and 151 is 16912.
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 112 and 151?
First, calculate the GCD of 112 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 151 = 0 remainder 112 |
| 2 | 151 ÷ 112 = 1 remainder 39 |
| 3 | 112 ÷ 39 = 2 remainder 34 |
| 4 | 39 ÷ 34 = 1 remainder 5 |
| 5 | 34 ÷ 5 = 6 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 13 | 1261 |
| 135 and 59 | 7965 |
| 41 and 138 | 5658 |
| 160 and 115 | 3680 |
| 104 and 119 | 12376 |