Problems on H.C.F and L.C.M - 01

Explanation:-

The greatest 4 digits number is 9999
The LCM of 12, 18, 21, 28 is 252
On dividing 9999 by 252 the remainder comes out to 171
Required number = 9999 - 171 = 9828

Explanation:-

Let the numbers are 3x and 4x
So HCF = x
∴ HCF × LCM = Product of numbers
⇒ x × 120 = 3x × 4x
⇒ x × 120 = 12x²
⇒ 120 = 12x
x = 10
∴ Numbers are 30 and 40
∴ Sum of two numbers = 30 + 40 = 70

Explanation:-

Number of pair of positive integers whose sum is 99 and HCF is 9 is (9, 90) (18, 81) (27, 72) (36, 63) (45, 54)

Explanation:-

The greatest length of pipes of same size will be HCF of 1.5 m and 1.2 m.
So HCF of 15 and 12 is 3, then HCF of 1.5 and 1.2 is 0.3 m

Explanation:-

The given three numbers are 2a, 5a and 7a
LCM of 2a, 5a and 7a = 2 × 5 × 7 × a = 70a

Explanation:-

210 = 21 × 10 = 7 × 3 × 2 × 5
take 2 and 3 with together then we find number is 5, 6, 7 which is consecutive number
so, 1^st + 2^nd = 5 + 6 = 11

Explanation:-

x, x + 1, x + 2, x + 3
1^st + 2^nd = 4^th x + x + 1 = x + 3
x = 2
2, 3, 4, 5
= 2 + 3 + 4 + 5 = 14

Explanation:-

HCF of 132, 204 and 228
132 = 2 × 2 × 3 × 11
204 = 2 × 2 × 3 × 17
228 = 2 × 2 × 3 × 19
∴ HCF of 132, 204 and 228 is 223 i.e. 12
∴ Required HCF = 12

Explanation:-

LCM of 24, 36, 48 = 144
So, the three girls will meet at one point in 144 seconds
i.e., 2 minutes 24 seconds

Explanation:-

LCM of 12, 18, 21, 32 = 2016
2016 × K = 2016 × 2 = 4032(K = 2)
"4032" is the number which is completely divided by 12, 18, 21, 32