Let the numbers are y and z then,
LCM x HCF = 1st Number x 2nd number
2772 x 99 = y x z
In such types of questions, try to make pair of numbers so that HCF could be 99.
198 and 1389 are the numbers having HCF be 99
∴ LCM =

LCM = 5HCF
The product of two numbers = LCM x HCF
720 = LCM x HCF
720 = 5HCF x HCF

LCM = 14 HCF
since LCM + HCF = 600
or 14 HCF + HCF = 600
or, HCF =

Let the numbers are 13 y and 15y. Hence, y will be their HCF
Now, as per rule, the product of two number = HCF x LCM
13y x 15y = y x 39780
∴ y =

Shortcut:
To find the greatest number that will exactly divide x, y and z will be given by HCF of x, y and z
Using this short cut, we get
HCF of 1365, 1560 and 1755 = 195

Shortcut:
To find the greatest number that will divide x, y and z leaves remainder a,b and c respectively. ∴ Required number = HCF of (x-a), (y-b) and (z - c)
Using the shortcut, we get
HCF of (38-2), (45-3) or (52-4)
or 36, 42 and 48 = 6

Shortcut:
To find the least number which is exactly divisible of x, y and z.
∴ Required number = LCM of x, y and z
Using the shortcut, we get
The required least number = LCM of 8, 12, 15 and 21 = 840

LCM of 48, 60, 64 = 960
The maximum four digit number is 9999
Divide 9999 by 960, we get remainder = 399
∴ 9999 - 399 = 9600

LCM of 27, 35, 25 and 21 = 4725
∴ the required no. = 4725 - 3 = 4722

LCM of 36, 48, 21 and 28 = 1008
∴ 1008 - 5 = 1013