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 (m=2^2\times3^a\times5) and (n=2^4\times3^3\times5^b\times13) have LCM (2^4\times3^5\times5^2\times13), which values are correct?HardLevel 12What is the smallest number that leaves remainder (7) when divided by (40), (54), and (72)?HardLevel 12If the HCF of (96), (144), and (240) is found, what will be the power of (2) in it?HardLevel 12If two numbers are coprime and their product is (437), what will be their LCM?HardLevel 12If (165=3\times5\times11) and (231=3\times7\times11), what is the sum of their HCF and LCM?HardLevel 12A number is divisible by both (2^5\times3^2\times11) and (2^3\times3^4\times5). What will be the power of (3) in the smallest such number?HardLevel 12If the HCF of two numbers is (27) and their LCM is (1215), and the numbers are taken as (27r) and (27s), what is the value of (rs)?HardLevel 12Which statement is correct for (112) and (168)?HardLevel 12If (A=2^4\times3\times5^2) and (B=2^2\times3^3\times5), what will be the power of (5) in their LCM?HardLevel 12If the LCM of (45), (60), and (84) is found, how many distinct prime factors will it have?HardLevel 12If the HCF of two numbers is (32) and their LCM is (768), what is the total power of (2) in their product?HardLevel 12The HCF of two numbers is (32) and their LCM is (768). What will be the total power of (2) in their product?HardLevel 12If ropes of (72) metres and (120) metres are to be cut into equal pieces of maximum length, what will be the length of each piece?HardLevel 12What is the smallest number exactly divisible by (25), (40), and (64)?HardLevel 12If (H) is the HCF and (L) is the LCM of (2^3\times3^2\times5) and (2^5\times3\times7), what is (LH) equal to?HardLevel 12If (a=2^2\times3^3\times5) and (b=2^4\times3\times5^2), what will be the power of (3) in their HCF?HardLevel 12If the HCF of two numbers is (18) and their LCM is (810), what will be their product?HardLevel 12If (54), (90), and (126) are to be divided by the same greatest possible number, what is that number?HardLevel 12If (H) is the HCF of (63), (105), and (147), what is the value of (H)?HardLevel 12What is the LCM of (88), (132), and (220)?HardLevel 12