Least Common Multiple (LCM) of 150 and 53
The least common multiple (LCM) of 150 and 53 is 7950.
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 53?
First, calculate the GCD of 150 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 53 = 2 remainder 44 |
| 2 | 53 ÷ 44 = 1 remainder 9 |
| 3 | 44 ÷ 9 = 4 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 67 | 13132 |
| 35 and 176 | 6160 |
| 123 and 22 | 2706 |
| 131 and 166 | 21746 |
| 172 and 21 | 3612 |