Least Common Multiple (LCM) of 150 and 196
The least common multiple (LCM) of 150 and 196 is 14700.
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 150 and 196?
First, calculate the GCD of 150 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 196 = 0 remainder 150 |
| 2 | 196 ÷ 150 = 1 remainder 46 |
| 3 | 150 ÷ 46 = 3 remainder 12 |
| 4 | 46 ÷ 12 = 3 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 69 | 276 |
| 70 and 108 | 3780 |
| 119 and 112 | 1904 |
| 132 and 148 | 4884 |
| 51 and 87 | 1479 |