Answer:
[tex] \color{orange}{1803} [/tex]
Step-by-step explanation:
Let the number be 'x'
Using the general formula
Divided number = (Quotient × Dividend) + Remainder
Where Quotient is an integer
When divided by 24..
x = 24P + 3
Where P is an integer
When divided by 36..
x = 30Q + 3
Where Q is an integer
When divided by 50..
x = 50R + 3
Where R is an integer
Therefore..
24P = 36Q = 50R
L.C.M of their co-oficients is 1800
[tex]1800 \frac{P}{75} =1800 \frac{Q}{50} =1800 \frac{R}{36} [/tex]
[tex] \frac{P}{75}=\frac{Q}{50} =\frac {R}{36}[/tex]
For smallest values for integers P, Q and R
P = 75, Q= 50 and R = 36
Substitute any of the values to find x
x = 24P + 3
x = 24(75) + 3
x = 1800 + 3
x = 1803
Hope it helps
