Least Common Multiple (LCM) of 150 and 35
The least common multiple (LCM) of 150 and 35 is 1050.
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 35?
First, calculate the GCD of 150 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 35 = 4 remainder 10 |
| 2 | 35 ÷ 10 = 3 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 192 | 7872 |
| 131 and 33 | 4323 |
| 108 and 63 | 756 |
| 147 and 148 | 21756 |
| 119 and 128 | 15232 |