lcm and hcf Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Answer: (a)

Bells will toll together again at a time, which is obtained by taking L.C.M. of their individual tolling intervals.

L.C.M. of 9, 12 and 15 = 180 min

They will toll together again after 180 min, i.e. 3 hours.

Time = 8 + 3 = 11 a.m.

Answer: (c)

LCM of 2, 3, 5 = 30

30 is least number which is divided by 2, 3 and 5.

The number of which gives reminder = 30 + 1 = 31.

Answer: (b)

For the least number of tiles to pave the floor, the size of tiles should be maximum.

∴ Side of tiles = HCF of 999 and 407 = 37 cm

∴ Required number of tiles = ${999 × 407}/{37 × 37}$ = 297

Answer: (d)

ATQ

${27 - x}/{35 - x} = 2/3$

81 – 3x = 70 – 2x

x = 11

Answer: (b)

HCF $(a/{HCF (a, b)}, b/{HCF (a, b)})$

= ${HCF (a, b)}/{LCM (HCF (a, b), HCF (a, b))} = {HCF (a, b)}/{HCF (a, b)}$ = 1

Example 1: a = 12 and b = 24

HCF of $({12}/{HCF (12, 24)}, {24}/{HCF (12, 24)})$

= HCF , $({12}/{12} , {24}/{12})$ = HCF (1, 2) = 1.

Example 2: a = 19, b = 23

HCF of $({19}/{HCF (19, 23)}, {23}/{HCF (19, 23)})$

= HCF of $({19}/1 , {23}/1)$

= HCF of (19, 23) = 1