# Worksheet on H.C.F. and L.C.M.

We will solve different types of problems given in the Worksheet on H.C.F. and L.C.M.

I. Fill in the blanks:

(i) The HCF of two numbers is 1, they are called ……………. numbers.

(ii) The LCM of two or more numbers cannot be ……………. than any one of the numbers.

(iii) The HCF of the given numbers cannot be ……………. than the number themselves.

(iv) The HCF of 7 and 35 is …………….

(v) The LCM of 7 and 35 is …………….

II. Find highest common factor of the following by complete factorisation:

(i) 48, 56, 72

(ii) 198, 360

(iii) 102, 68, 136

(iv) 1024, 576

(v) 405, 783, 513

III. Find the H.C.F. by long division method:

(i) 84, 144

(ii) 120, 168

(iii) 430, 516, 817

(iv) 632, 790, 869

(v) 291, 582, 776

(vi) 219, 1321, 2320, 8526

IV. Find lowest common multiple of the following numbers:

(i) 16, 24, 40

(ii) 40, 56, 60

(iii) 207, 138

(iv) 72, 96, 120

(v) 120, 150, 135

(vi) 102, 170, 136

V. The LCM of two numbers is 60. If the product of the two numbers is 180, find their HCF.

VI. The HCF of two numbers is 40. If the product of the two numbers is 52800, find their LCM.

VII. The HCF and LCM of two numbers is 5 and 30 respectively. If one of the numbers is 10, find the other number.

Note: LCM × HCF = Product of numbers

Answers for the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) are given below.

I. (i) Co-prime

(ii) less

(iii) greater

(iv) 7

(v) 35

II. (i) 8

(ii) 18

(iii) 34

(iv) 64

(v) 27

III. (i) 12

(ii) 24

(iii) 43

(iv) 79

(v) 97

(vi) 1

IV. (i) 240

(ii) 840

(iii) 414

(iv) 1440

(v) 5400

(vi) 2040

V. 3

VI. 1320

VII. 15

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