Least Common Multiple (LCM) of 180 and 70
The least common multiple (LCM) of 180 and 70 is 1260.
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 180 and 70?
First, calculate the GCD of 180 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 70 = 2 remainder 40 |
| 2 | 70 ÷ 40 = 1 remainder 30 |
| 3 | 40 ÷ 30 = 1 remainder 10 |
| 4 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 73 | 11680 |
| 171 and 178 | 30438 |
| 171 and 61 | 10431 |
| 35 and 152 | 5320 |
| 57 and 38 | 114 |