192 = 2^6 × 3
2^2 × 3 = 12 & 2^4 = 16 are in the ratio 3:4 (Factors of 192 are used here)
LCM of 12 and 16 is 16.
Now since
12 = 2^2 × 3 and 16 = 2^4 and LCM of the unknown numbers = 192 = 2^6 × 3, the number that can be multiplied to 12 & 16 (to keep the ratio 3:4) is 2^2 (LCM is the product of the highest exponent of all the unique prime factors of the numbers. Since we already have 3 all we need now is 2^6 which can be achieved by multiplying both numbers with 4 (2^2))
12 × 4 = 48 = 2^4 × 3
16 × 4 = 64 = 2^6
48 : 64 :: 3 : 4.
