Mathematics

HCF and LCM using prime factorisation

अभाज्य गुणनखंडन द्वारा महत्तम समापवर्तक और लघुत्तम समापवर्त्य

In this Class 10 Mathematics topic from Real Numbers, students learn to find the HCF and LCM of two or more numbers through prime factorisation. They break each number into prime factors, compare the resulting powers, and select the appropriate common factors: the lowest powers for HCF and the highest powers for LCM. The topic also develops accuracy in writing factor trees, simplifies comparison between methods, and helps students apply these concepts to numerical and everyday problem-solving situations.

Practice questions

01 If two numbers are coprime and their product is (1147), what will be their LCM?

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Answer and explanation

HCF and LCM using prime factorisation

Practice questions

01 If two numbers are coprime and their product is (1147), what will be their LCM?

02 The prime factorisations of three numbers are (2^4\times3^2\times5), (2^2\times3^3\times7), and (2^5\times3\times11). What will be their HCF?

03 If the LCM of (68), (85), and (289) is found, what will be the power of (17) in it?

04 The HCF of two numbers is (21) and their LCM is (2310). How many unordered pairs are possible?

05 If the HCF of two numbers is (75) and their LCM is (1950), what is correct about their existence?

06 If the HCF of (132) and (220) is (44), what will be the power of (5) in their LCM?

07 A number is divisible by both (2^5\times3^4\times5) and (2^7\times3^2\times11). What will be the smallest such number?

08 If the HCF of (2^a\times3^3\times5) and (2^6\times3^5\times5^2) is (2^4\times3^3\times5), which value of (a) is possible?

09 If the LCM of (2^4\times3^b\times7) and (2^5\times3^3\times7^2) is (2^5\times3^6\times7^2), what can be the value of (b)?

10 If (a) and (b) are coprime, (a=2^4\times3), and (ab=2496), what is (b)?

11 If (L) is the LCM of (98), (147), and (245), what is the value of (L)?

12 If a number leaves remainder (15) when divided by (40), (56), and (88), what is the smallest such number?

13 If the LCM of (2^5\times3^3), (2^7\times3^2\times5), and (2^4\times3^5\times7) is found, what will be the power of (2) in it?

14 The HCF of two numbers is (33) and their LCM is (2145). If one number is (165), what is the other number?

15 A number leaves remainder (0) when divided by (168), (210), and (280). What is the smallest such number?

16 If (a=2^7\times3^2\times5^3) and (b=2^4\times3^5\times5), what will be the power of (5) in their HCF?

17 If (L) is the LCM and (H) is the HCF of (2^6\times3^2\times5) and (2^3\times3^6\times5^2), what will be the powers of (3) in (L) and (H) respectively?

18 Which pair has HCF (26) and LCM (2860)?

19 If (288=2^5\times3^2) and (432=2^4\times3^3), the product of their LCM and HCF will be equal to what?

20 If (H) is the HCF of (143), (187), and (253), what is the value of (H)?

21 If the LCM of (2^5\times3^5\times5), (2^7\times3^2\times7), and (2^4\times3^4\times11) is found, what will be the power of (3) in it?

22 The HCF of two numbers is (81) and their LCM is (4617). If the numbers are taken as (81r) and (81s), what is the value of (rs)?

23 If (H) is the HCF and (L) is the LCM of (2^7\times3^3\times5^2) and (2^4\times3^6\times5), what is (\frac{L}{H})?

24 If (H) and (L) are respectively the HCF and LCM of (330), (462), and (770), what is (L\div H)?

25 If (L) is the LCM of (2^5\times3^4\times5) and (2^7\times3^2\times5^3\times17), how many distinct prime factors will (L) have?

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