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 (L) is the LCM of (108), (162), and (270), what is the value of (L)?HardLevel 13A number leaves remainder (11) when divided by (32), (48), and (72). Which is the smallest such number?HardLevel 13If the LCM of (2^a\times3^3\times5) and (2^4\times3^2\times5^2) is (2^6\times3^3\times5^2), which value of (a) is possible?HardLevel 13The HCF of two numbers is (28) and their product is (70560). What will be their LCM?HardLevel 13If the HCF of (154) and (231) is (77), what will be their LCM?HardLevel 13Which option correctly gives the HCF of (2^5\times3^2\times11) and (2^3\times3^4\times11^2)?HardLevel 13If (H) is the HCF of (91), (143), and (187), what is the value of (H)?HardLevel 13If (H) is the HCF of (91), (143), and (187), what is the correct value of (H)?HardLevel 13If (L) is the LCM of (2^4\times3\times5^2) and (2^2\times3^3\times5), what will be the power of (3) in (L)?HardLevel 13If the HCF of two numbers is (15) and their LCM is (420), what is correct about their existence?HardLevel 13The HCF of two numbers is (21) and their LCM is (1386). If one number is (198), what is the other number?HardLevel 13If the HCF of (120), (180), and (300) is found, what will be the power of (2) in it?HardLevel 13If the LCM of (48), (75), and (125) is found, what will be the power of (5) in it?HardLevel 13If the prime factorisations of two numbers are (2^6\times3^4\times5) and (2^4\times3^2\times5^3\times7), what will be their HCF?ExpertLevel 10The prime factorisations of three numbers are (2^3\times3^2\times11), (2^5\times3\times5), and (2^2\times3^4\times7). What will be their LCM?ExpertLevel 10The HCF of two numbers is (36), their LCM is (1620), and one number is (180). What is the other number?ExpertLevel 10If (a=2^5\times3^3\times7) and (b=2^2\times3^5\times5\times7^2), what is the value of (\frac{\text{LCM}}{\text{HCF}})?ExpertLevel 10If the HCF of two numbers is (24) and their LCM is (1320), which statement about their existence is correct?ExpertLevel 10The HCF of two numbers is (18) and their LCM is (1260). How many unordered pairs of such numbers are possible?ExpertLevel 10What is the smallest number that leaves remainder (13) when divided by (42), (56), and (70)?ExpertLevel 10