AMCAT HCF AND LCM Quiz-1

HCF \times LCM = Product of two numbers
=> 8 \times LCM = 1280
=> LCM = \frac{1390}{5}
=278

Ans: 80, 96
H.C.F. of the two 2-digit numbers= 16
Hence, the numbers can be expressed as 16x and 16y, where x and y are prime to each other.
Now,
First number \times second number = H.C.F. \times L.C.M.
=> 16x \times 16y = 16 \times 480
=> xy = 16 \times \frac{480}{16} \times 16= 30 ´
The possible pairs of x and y, satisfying the condition xy = 30 are :
(3, 10), (5, 6), (1, 30), (2, 15)
So the numbers are (48,160) (80,96)

The greatest number of five digits is 99999.
LCM of 3, 5, 8 and 12
=> 2 \times 2 \times 3 \times 5 \times 2 = 120
After dividing 99999 by 120, we get 39 as remainder
99999 – 39 = 99960
99960 is the greatest five digit number divisible by the given divisors.
In order to get 2 as remainder in each case we will simply add 2 to 99960.
therefore Greatest number = 99960 + 2 = 99962

LCM of 15, 12, 20, 54 = 540
Then number = 540 + 4 = 544
[4 being remainder]

Required time = LCM of 252, 308 and 198 seconds
LCM = 2 \times 2 \times 7 \times9 \times11
= 2772 seconds
= 46 minutes 12 seconds

LCM of = 8 \times 9 \times 5 \times 7 \times = 2520
The largest number of four digits= 9999
Greatest 4 digit number divisible by 15,18,21,24 = 2520×3 = 7560
Because
15 – 11 = 4
18 – 14 = 4
21 – 17 = 4
24 – 20 = 4
So, 7560 - 4 = 7556

Here 4 – 1 = 3, 5 – 2 = 3, 6 – 3 = 3
\therefore The required number
= LCM of (4, 5, 6) – 3
= 60 – 3 = 57

LCM of 4, 6, 10, 15 = 60
Least number of 6 digits = 100000
Dividing 100000 by 60 get we get 40
The least number of 6 digits which is exactly divisible by 60
= 100000 + (60 – 40)
= 100020
\therefore Required number (N)
= 100020 + 2 = 100022
Hence, the sum of digits = 1 + 0+ 0 + 0 + 2 + 2 = 5

The LCM of 12, 18, 21, 30
LCM = 2 \times 3 \times 2 \times 3 \times 7 \times 5
= 1260
\therefore The required number = 1260/2 = 630

LCM (10, 16, 24)
= 5 × 2 × 8 × 3 = 240
⇒ for square number split the LCM into its factors
= 5 × 2 × 2 × 2 × 2 × 3
= 5 × 5 × 2 × 2 × 2 × 2 × 3 × 3
= 3600