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 (16) and their LCM is (640), what is their product?HardLevel 11If (a=2^3\times3^2\times5) and (b=2^5\times3\times5^2), what will be the power of (5) in their HCF?HardLevel 11Which statement is correct for (150) and (210)?HardLevel 11If two numbers are (2^3\times3\times7) and (2\times3^2\times5), what is their LCM?HardLevel 11If the product of two numbers is (15120) and their LCM is (420), what is their HCF?HardLevel 11If ropes of lengths (96) and (160) are to be cut into equal pieces of maximum length, what will be the maximum length of each piece?HardLevel 11If the HCF of (2^6\times3^2\times5) and (2^4\times3^5\times7) is (M), what is the value of (M)?HardLevel 11If the LCM of (40), (64), and (96) is found, what will be the power of (2)?HardLevel 11What is the smallest number exactly divisible by (27), (45), and (63)?HardLevel 11If the HCF of two numbers is (9) and their LCM is (180), which conclusion is correct?HardLevel 11The HCF of two numbers is (12), and the numbers are (12m) and (12n). If their LCM is (504), what is the value of (mn)?HardLevel 11If (A=2^3\times3^2\times5^2) and (B=2^4\times3\times5), what is (\frac{A\times B}{\text{HCF}}) equal to?HardLevel 11If (108=2^2\times3^3) and (180=2^2\times3^2\times5), what is the ratio of their LCM to HCF?HardLevel 11In a ground, (132) plants and (198) flags are to be arranged in equal rows. Each row should have the same number of each item separately, and the number of rows should be maximum. What is the maximum number of rows?HardLevel 11If the HCF of two numbers is (45) and their LCM is (1260), what is the correct statement about the existence of the two numbers?HardLevel 11Which number will be a multiple of both (2^5\times3^2\times5) and (2^3\times3^4\times7)?HardLevel 11If the HCF of two numbers is (21) and their LCM is (462), which pair is possible?HardLevel 11If the HCF of (2^a\times3^2) and (2^5\times3^4) is (2^3\times3^2), what is correct about (a)?HardLevel 11If the HCF of (72), (90), and (150) is found, what will be the power of (3)?HardLevel 11A number is divisible by (2^4\times3^2\times5) and also by (2^3\times3^4\times7). What will be the power of (3) in the smallest such number?HardLevel 11