MeritTrac LCM & HCF Questions and Answers Quiz-1

90207=3*3*3*13*257
127986=2*3*83*257
232585=5*181*257
Hence 257 is required number.

Video solution:

Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399.

Required number (9999 - 399) = 9600.

Since their HCFs are 7, numbers are divisible by 7 and are
of the form 7x and 7y

Difference = 14
=> 7x - 7y = 14
=> x - y = 2

product of numbers = product of their hcf and lcm
=> 7x * 7y = 441 * 7
=> x * y = 63

Now, we have
x * y = 63 , x - y = 2
=>x = 9 , y = 7

The numbers are 7x and 7y
=> 63 and 49

HCF of 42,49,63 is 7
so for 42 there will be 42/7=6
from 49 there will be 49/7=7
from 63 there will be 63/7=9
total no of planks 6+7+9=22 ans

Required number = (L.C.M. of 12,16, 18, 21, 28) + 7

= 1008 + 7

= 1015

Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.

Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.

lcm of 48,72,108
lcm=432
432/60=7.2
add 7min2sec to8:20:00
ans would be
8:27:12

product of numebrs = 5 x 120 = 600  factors = 5 x 5 x 3 x 2 x 2 x 2

sum is = 55

xy = 600

x + y = 55

reciprocal

1/x + 1/y = (x+y)/xy  = 55/600 = 11/120

hcf of 495,900,1665 45 cm