LCM OF 35,12,20
Let's start with the multiples of each number.
35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455 . . .
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432 . . .
20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440 . . .
What is the smallest number in those three lists?
Gee -- but that was a lot of work. I would have saved a lot of time if I'd multiplied 35 times 12 = 420. Since it is also divisible by 20 -- that must be the answer.
http://www.helpwithfractions.com/least-common-multiple.html
420 because
35=5 x 7
12=3 x 2 x 2
20=2 x 2 x 5
= 5 x 7 x 3 x 2 x 2
To find the LCM (Least Common Multiple) of three numbers, you can follow these steps:
1. Prime factorize each number. Write each number as a product of its prime factors.
35 = 5 × 7
12 = 2 × 2 × 3
20 = 2 × 2 × 5
2. Identify all the unique prime factors from the prime factorization of each number.
Prime factors: 2, 3, 5, 7
3. Take the highest power of each prime factor.
2^2, 3^1, 5^1, 7^1
4. Multiply all these prime factors together.
2^2 × 3^1 × 5^1 × 7^1 = 2 × 2 × 3 × 5 × 7 = 420
Therefore, the LCM of 35, 12, and 20 is 420.