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 (a=2^5\times3^2\times11) and (b=2^3\times3^4\times5), what is the value of (\frac{\text{LCM}}{\text{HCF}})?HardLevel 10What is the smallest number exactly divisible by (24), (36), and (54)?HardLevel 10What is the greatest number that can exactly divide (168), (252), and (420)?HardLevel 10Two numbers are (2^4\times3^2) and (2^2\times3\times5^2). The product of their HCF and LCM will be equal to what?HardLevel 10If (x=2^a\times3^4\times5) and (y=2^3\times3^b\times7) have HCF (2^2\times3^2), which statement about (a) and (b) is correct?HardLevel 10If the HCF of two numbers is (12) and their LCM is (420), which pair can be such numbers?HardLevel 10A school has (72) boys and (96) girls. They must be arranged in separate rows with the same number of students in each row, and this number must be maximum. How many students will be in each row?HardLevel 10Three bells ring at intervals of (18), (24), and (30) seconds respectively. If they ring together now, after how many seconds will they ring together again?HardLevel 10If the LCM of two numbers is (2^5\times3^3\times5) and their HCF is (2^2\times3), what is the power of (2) in the product of the two numbers?HardLevel 10If two numbers are coprime and their product is (391), what is their LCM?HardLevel 10Which of the following numbers is divisible by both (2^3\times3^2\times5) and (2^2\times3^4\times7)?HardLevel 10Two numbers are (180) and (252). What is their HCF in prime factor form?HardLevel 10If (96=2^5\times3) and (144=2^4\times3^2), what is the LCM of (96) and (144)?HardLevel 10A number (N) has prime factorisation (2^4\times3^2\times5). What is the HCF of (N) and (2^3\times3^5\times7)?HardLevel 10If the HCF of two numbers is (15) and their LCM is (630), what is the product of the two numbers?HardLevel 10If (A=2^2\times3\times5^3) and (B=2^5\times3^2\times5), which prime factor will have power (3) in the LCM?HardLevel 10A shopkeeper has (126) red pens and (210) blue pens. He wants to make the maximum number of identical packets so that each packet has the same number of red pens and the same number of blue pens. How many packets can he make?HardLevel 10What is the smallest number that leaves remainder (0) when divided by (45), (60), and (75)?HardLevel 10The HCF of two numbers is (2^2\times3) and their LCM is (2^4\times3^3\times5). If one number is (2^4\times3\times5), what is the other number?HardLevel 10If two numbers have no common prime factor in their prime factorisations, which statement about their HCF is correct?HardLevel 10