The LCM of two numbers is 2376 while their HCF is 33. If one of the number is 297, then the other number is

LCM of two coprimes is equal to their product.

Required HCF = (HCF of numerators) / (LCM of denominators)
= (HCF of 1, 3 and 4) / (LCM of 2, 4, and 5)
= 1/20

We know that,
HCF of fractions = (HCF of numerators) / (LCM of denominators)
? Required HCF = (HCF of 4 and 7) / (LCM of 5 and 15)
=1/15

132 = 2 x 2 x 3 x 11
240 = 2 x 2 x 2 x 2 x 3 x 5
228 = 2 x 2 x 3 x 19

Hence, HCF of 132, 204 and 228 = 2 x 2 x 3 = 12

LCM of (12,18, 36) = 36
? A number greater than 300 on dividing by 36 leaves a remainder 4 = (36 x 9) + 4 = 328
Next numbe r = 328 + 36 = 364
? Sum of number = 328 + 364 = 692

Given,
LCM = 1989, HCF = 13
1st number = 117 and
2nd number = ?

According to the formula,
Product of LCM and HCF = Product of two numbers
? 1989 x 13 = 117 x ?
? = (1989 x 13)/117
? = 221

Let the numbers are 3N, 4N and 5N.
Where, N = HCF
Then, LCM = 60N

According to the question,
60N = 1200
? N = 20

Let numbers be 10N, 12N, 15N and 18N.
Then, LCM = 180N and HCF = N
Hence, required LCM = 180 x 3 = 540

By Hit and Trial
From option (d), we can say that the HCF of 36 and 24 is 12 and it is also satisfies the given condition
a > b > 12
? a = 36 and b = 24

Let LCM = m, HCF = n,

According to the question,
m = 12n, .......(i)
and m + n = 403.......(ii)
? 12n + n = 403 [from Eq.(i)]
? 13n = 403
? n = 403/13 = 31
? m = 12 x 31 = 372

Let the another number = k
? 93 x k = 372 x 31
[as product of two numbers HCF x LCM]
? k = (372 x 31)/93 = 124