
Shortcut Trick
Convert all numbers to have the same number of decimal places: 5.00, 8.30, and 0.19.
Treat them as integers by removing the decimal: 500, 830, and 19.
Find the LCM of 500, 830, and 19:
LCM(500, 830, 19) = 10 × 50 × 83 × 19 = 788500.
Adjust the decimal point back by 2 places: 788500 ÷ 100 = 7885.
∴ The correct answer is 7885.

Alternate Method
Given: The numbers are 5, 8.3, and 0.19.
Formula Used: LCM of Fractions = LCM of Numerators ÷ HCF of Denominators.

⇒ Write the numbers as fractions with a common denominator: 5 = 500/100, 8.3 = 830/100, 0.19 = 19/100.
⇒ Numerators: 500, 830, 19. Denominators: 100, 100, 100.
⇒ Factorize numerators: 500 = 22 × 53 | 830 = 2 × 5 × 83 | 19 = 19 (Prime).
⇒ LCM(500, 830, 19) = 22 × 53 × 83 × 19.
⇒ LCM(500, 830, 19) = 4 × 125 × 83 × 19 = 500 × 1577 = 788500.
⇒ HCF of denominators = HCF(100, 100, 100) = 100.
⇒ LCM of decimals = 788500 ÷ 100 = 7885.
∴ The correct answer is 7885.

Additional Information
LCM of Fractions
The LCM of a set of fractions is calculated as LCM of Numerators ÷ HCF of Denominators.
HCF of Fractions
The HCF of a set of fractions is calculated as HCF of Numerators ÷ LCM of Denominators.
Like Decimals
To find the LCM or HCF of decimals, always convert them to like decimals (same number of decimal places) first to avoid calculation errors.
Co-prime Numbers
If a set of numbers contains prime numbers that do not divide the other numbers, the LCM will include those primes as direct factors.