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
If the HCF of two numbers is (54) and their LCM is (1890), what is correct about their existence?ExpertLevel 10If the HCF of (120) and (168) is (24), what will be the power of (7) in their LCM?ExpertLevel 10A number is divisible by both (2^4\times3^3\times5) and (2^6\times3\times7). What will be the smallest such number?ExpertLevel 10If the HCF of (2^a\times3^2\times7) and (2^5\times3^4\times7^2) is (2^3\times3^2\times7), which value of (a) is possible?ExpertLevel 10If the LCM of (2^3\times3^b\times5) and (2^4\times3^2\times5^3) is (2^4\times3^5\times5^3), what can be the value of (b)?ExpertLevel 10If (a) and (b) are coprime, (a=2^3\times5), and (ab=1720), what is (b)?ExpertLevel 10A number leaves remainders (31), (43), and (55) when divided by (36), (48), and (60) respectively. What is the smallest such number?ExpertLevel 10If the LCM of (2^4\times3^3), (2^6\times3^2\times5), and (2^5\times3^4\times7) is found, what will be the power of (2) in it?ExpertLevel 10The HCF of two numbers is (27) and their LCM is (1701). If one number is (189), what is the other number?ExpertLevel 10A number leaves remainder (0) when divided by (144), (180), and (216). What is the smallest such number?ExpertLevel 10If (a=2^6\times3\times5^2) and (b=2^3\times3^4\times5), what will be the power of (5) in their HCF?ExpertLevel 10If (L) is the LCM and (H) is the HCF of (2^5\times3^2\times5) and (2^2\times3^5\times5^2), what will be the powers of (3) in (L) and (H) respectively?ExpertLevel 10Which pair has HCF (22) and LCM (1848)?ExpertLevel 10If (216=2^3\times3^3) and (360=2^3\times3^2\times5), the product of their LCM and HCF will be equal to what?ExpertLevel 10If (H) is the HCF of (99), (165), and (231), what is the value of (H)?ExpertLevel 10If the LCM of (2^3\times3^4\times5), (2^5\times3^2\times7), and (2^4\times3^3\times11) is found, what will be the power of (3) in it?ExpertLevel 10If the HCF of two numbers is (63) and their LCM is (2079), and the numbers are taken as (63r) and (63s), what is the value of (rs)?ExpertLevel 10If (H) is the HCF and (L) is the LCM of (2^6\times3^2\times5^2) and (2^4\times3^5\times5), what is (\frac{L}{H})?ExpertLevel 10If (H) and (L) are respectively the HCF and LCM of (252), (315), and (420), what is (L\div H)?ExpertLevel 10If (L) is the LCM of (2^4\times3^3\times5) and (2^6\times3\times5^2\times13), how many distinct prime factors will (L) have?ExpertLevel 10