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) and (b) are coprime, (a=2^2\times5), and (ab=420), what is (b)?HardLevel 11If the HCF of two numbers is (2^2\times3) and their LCM is (2^5\times3^3\times5), what will be the power of (3) in their product?HardLevel 11Which option correctly gives the HCF of (48), (72), and (108)?HardLevel 11Which option correctly gives the LCM of (54), (81), and (135)?HardLevel 11If the HCF of two numbers is (28), their LCM is (840), and one number is (140), what is the other number?HardLevel 11If the HCF of two numbers is (20) and their product is (24000), what is their LCM?HardLevel 11If the HCF of (75) and (125) is called (H) and their LCM is called (L), what is (L-H)?HardLevel 11If (2^4\times3^2\times5) is the LCM and (2^2\times3) is the HCF, what is (\frac{\text{LCM}}{\text{HCF}})?HardLevel 11The HCF of two numbers is (6), and the numbers are (6r), (6s). If (r=7) and (s=8), what is their LCM?HardLevel 11If (L) is the LCM of (2^3\times3^2) and (2^5\times3\times11), what will be the power of (11) in (L)?HardLevel 11A number (N) leaves remainder (0) when divided by (36), (54), and (90). What is the smallest possible value of (N)?HardLevel 11If the prime factorisations of two numbers are (2^6\times3\times5^2) and (2^4\times3^3\times5\times11), what will be their HCF?HardLevel 13What is the LCM of (84), (126), and (198)?HardLevel 12The product of two numbers is (30240) and their HCF is (42). What will be their LCM?HardLevel 12If (a=2^3\times3^4\times7) and (b=2^5\times3^2\times5\times7^2), what is (\frac{\text{LCM}}{\text{HCF}})?HardLevel 12A warehouse has (156) bags of rice and (234) bags of wheat. They are to be divided into the maximum number of identical groups so that each group has the same number of both types of bags. How many groups can be made?HardLevel 12Four signal lights flash at intervals of (12), (18), (27), and (36) seconds. They flash together now. After how many seconds will they flash together again?HardLevel 12If the HCF of two numbers is (35), their LCM is (1470), and one number is (210), what is the other number?HardLevel 12Which pair has HCF (14) and LCM (910)?HardLevel 12If (x=2^a\times3^3\times11) and (y=2^5\times3^b\times7) have HCF (2^4\times3^2), which values are possible?HardLevel 12