Robert Bosch LCM & HCF Quiz-3

Here, Divisor – remainder = 1
e.g., 10 – 9 = 1, 9 – 8 = 1,
8 – 7 = 1
\therefore Required number
= (L.C.M. of 10, 9, 8) –1
= 360 – 1 = 359

We will find the LCM of 16, 24, 30 and 36.
\therefore LCM = 2 \times 2 \times 2 \times 3\times 2 \times 5 \times 3 = 720
The largest number of five digits
= 99999
On dividing 99999 by 720, the remainder = 639
\therefore The largest five-digit number divisible by 720
= 99999 – 639 = 99360
\therefore Required number = 99360 + 10
= 99370

LCM of 3, 5, 6, 8, 10 and 12
= 120
\therefore Required number
= 120x + 2, which is exactly divisible by 13.
120x + 2 = 13 \times 9x + 3x + 2
Clearly 3x + 2 should be divisible by 13.
For x=8,3x + 2 is divisible by 13.
\therefore Required number
= 120x + 2 = 120 \times 8 + 2
= 960 + 2 = 962

LCM of 9, 10 and 15 = 90
=> The multiple of 90 are also divisible by 9, 10 or 15.
\therefore 21 * 90 = 1890 will be divisible by them.
\therefore Now, 1897 will be the number that will give the remainder 7.
= 1936 – 1897
Required number
= 1936 – 1897 = 39

The LCM of 5, 6, 7 and 8 = 840
\therefore Required number = 840 k +3 which is exactly divisible by 9 for some value of k.
Now, 840 k + 3 = 93 \times 9 k + (3k+ 3)
When k = 2, 3k + 3 = 9, which is divisible by 9.
\therefore Required number
= 840 \times 2 + 3 = 1683

LCM of 15, 20 and 35 = 420
\therefore Required least number = 420 + 8 = 428

Here,12 – 2 = 10; 16 – 6 = 10; 24 – 14 = 10
Now, LCM of 12, 16 and 24 = 48
\therefore The greatest 4–digit number exactly divisible by 48 = 9984
\therefore Required number
= 9984 – 10 = 9974

LCM of 24, 36 and 54 seconds
= 216 seconds
= 3 minutes 36 seconds
\therefore Required time = 10 : 15 : 00 + 3 minutes 36 seconds
= 10 : 18 : 36 a.m.

A makes one complete round of the circular track in \frac{5}{(\frac{5}{2}) }
= 2 hours
B in \frac{5}{3}[/ latex] hours and C in \frac{5}{2} hours.
That is after 2 hours A is at the starting point, B after \frac{5}{3} hours and C after \frac{5}{2} hours.
Hence the required time
= LCM of 2, \frac{5}{3} and \frac{5}{2} hours
= \frac{LCM of 2, 5, 5}{HCF of 3, 2}
= \frac{10}{1}
= 10 hours.

Required time = LCM of 200,300, 360 and 450 seconds
= 1800 seconds