The LCM of the numbers 5, 8.3 and 0.19 is:

Concept: An LCM has to be a whole-number multiple of every given quantity, so it cannot be read off directly when the quantities are decimals. The standard method is to scale: multiply every number by the same power of ten, 10n, where n is the largest count of decimal places among them, so that all of them become integers. Take the LCM of those integers and then divide the result back by 10n. This is exact because multiplying a whole set of numbers by a common factor k multiplies their LCM by exactly the same factor k.

Application: Apply this to 5, 8.3 and 0.19.

1. Count the decimal places: 5 has 0, 8.3 has 1 and 0.19 has 2. The largest count is 2, so the scaling factor is 102 = 100.

2. Scale every number by 100: 5 × 100 = 500, 8.3 × 100 = 830 and 0.19 × 100 = 19.

3. Factorise the scaled integers: 500 = 22 × 53, 830 = 2 × 5 × 83, and 19 is prime.

4. Take the highest power of each prime that appears anywhere: LCM(500, 830, 19) = 22 × 53 × 19 × 83 = 4 × 125 × 1577 = 788500.

5. Divide back by the scaling factor: 788500 ÷ 100 = 7885.

Cross-check: Test the value against each original number: 7885 ÷ 5 = 1577, 7885 ÷ 8.3 = 950 and 7885 ÷ 0.19 = 41500. All three quotients are whole numbers, so 7885 is a common multiple. It is also the least one, because a smaller common multiple would, after scaling by 100, give a common multiple of 500, 830 and 19 below 788500, and no such number exists.

Result: The LCM of 5, 8.3 and 0.19 is 7885.